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		<title>wsdl webservice from Outlook Web App</title>
		<link>http://gbideas.wordpress.com/2011/08/01/wsdl-webservice-from-outlook-web-app/</link>
		<comments>http://gbideas.wordpress.com/2011/08/01/wsdl-webservice-from-outlook-web-app/#comments</comments>
		<pubDate>Mon, 01 Aug 2011 15:42:45 +0000</pubDate>
		<dc:creator>gbideas</dc:creator>
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		<description><![CDATA[I&#8217;m trying to figure out what the Webservice for an Outlook Web App (OWA) can provide me with. So far, this doesn&#8217;t work but I hope I&#8217;ll manage to get it to work during this post. I had the URL for webservice. It look something like this: https://exchange.myuniversity.edu/EWS/Services.wsdl Then I wanted to create the client-class-stubs [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=gbideas.wordpress.com&amp;blog=7643295&amp;post=250&amp;subd=gbideas&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>I&#8217;m trying to figure out what the Webservice for an Outlook Web App (OWA) can provide me with.</p>
<p>So far, this doesn&#8217;t work but I hope I&#8217;ll manage to get it to work during this post.</p>
<p>I had the URL for webservice. It look something like this:</p>
<pre>https://exchange.myuniversity.edu/EWS/Services.wsdl</pre>
<p>Then I wanted to create the client-class-stubs via wsimport . I tried running wsimport from the command line.</p>
<p>First problem: I have to use a proxy. As wsimport works from the console I tried setting the proxy there. As I use Windows 7 proxycfg wasn&#8217;t the correct command any more but I had to use</p>
<pre>netsh winhttp set proxy proxy.mycompany.com:3128</pre>
<p>In case you have put explicity proxy information into the system settings of IE <a title="NETSH statt PROXYCFG.EXE für Windows Vista bei Problemen mit dem Windows-Update hinter einem Proxy - Offenes Forum Bauingenieurwesen - Bauforum für Studierende, Absolventen und Freunde der HS Bochum" href="http://bauforum.wirklichewelt.de/forum_entry.php?nr=3209">netsh winhttp import proxy source=ie</a> might help. But I only have an automatic configuration there and that didn&#8217;t carry over to the command line proxy configuration.</p>
<p>Then I figured that wsimport had it&#8217;s own proxy argument and I could get the result via:</p>
<pre>wsimport -httpproxy:proxy.mycompany.com:3128 https://exchange.myuniversity.edu/EWS/Services.wsdl</pre>
<p>This got me the following error message:</p>
<pre>[ERROR] Server returned HTTP response code: 401 for URL: https://exchange.myuniversity.edu/EWS/Services.wsdl,  "https://exchange.myuniversity.edu/EWS/Services.wsdl" needs authorization, please provide authorization file with read access at C:\Users\winusername\.metro\auth or use -Xauthfile to give the authorization file and on each  line provide authorization information using this format : http[s]://user:password@host:port//&lt;url-path&gt;</pre>
<p>So I created a file myuni.txt with the line:</p>
<pre>https://uniaccountname:unipassword@exchange.myuniversity.edu/EWS/Services.wsdl</pre>
<p>(At first I mistakenly thought that I was supposed to download the SSL certificate, but that wasn&#8217;t the case.)</p>
<p>I than ran:</p>
<pre>wsimport -httpproxy:proxy.mycompany.de:3128 -Xauthfile myuni.txt https://exchange.myuniversity.edu/EWS/Services.wsdl</pre>
<p>However I ran into:</p>
<pre>parsing WSDL...
[ERROR] Server redirected too many  times (20),  "https://exchange.myuniversity.edu/EWS/Services.wsdl" needs authorization, please provide authorization file with read access at C:\Users\winusername\.metro\auth or use -Xauthfile to give the authorization file and on each line provide authorization information using this format: http[s]://user:password@host:port//&lt;url-path&gt;</pre>
<p>I didn&#8217;t know how to solve this, so followed <a title="wsimport with amazon problem (SCDJWS forum at JavaRanch)" href="http://www.coderanch.com/t/520378/java-Web-Services-SCDJWS/certification/wsimport-amazon">Ravi C Kota&#8217;s suggestion on Code Ranch </a>to just download the wsdl-file.</p>
<p>However I than got:</p>
<pre> At least one WSDL with at least one service definition needs to be provided.
        Failed to parse the WSDL.</pre>
<p>Maybe I have the same problem as <a title="Exchange 2007 - Web Services - Standard compliance" href="http://social.technet.microsoft.com/forums/en-US/exchangesvrdevelopment/thread/98997214-e2d3-4582-9849-05a841e6f5ec">Henning Mahlzahn over at social.technet.microsoft.com</a>.</p>
<p>Unfortunately Henning Mahlzahn only links to the URL</p>
<p><a title="Former Link on How to Modify MS Echange Web Service Files for them to work with Java" href="http://tp.its.yale.edu/confluence/display/EXCH/Introduction+to+MS+Exchange+Web+Services+via+Java%28JAXWS%29">http://tp.its.yale.edu/confluence/display/EXCH/Introduction+to+MS+Exchange+Web+Services+via+Java%28JAXWS%29</a></p>
<p>saying it describes how to change the wsdl file. As this URL is down, I tried to figure out how to correct my wsdl by looking at the amazon.wsdl file at:</p>
<p><a title="Amazon Web Service wsdl" href="http://soap.amazon.com/schemas2/AmazonWebServices.wsdl">http://soap.amazon.com/schemas2/AmazonWebServices.wsdl</a></p>
<p>Infering from that file I added a service definition in my wsdl file before the last line and after the last &lt;/wsdl:binding&gt;. Including the two surrunding lines I had:</p>
<pre>    &lt;/wsdl:binding&gt;
    &lt;wsdl:service name="ExchangeService"&gt;
        &lt;wsdl:port name="ExchangeServicePortType" binding="tns:ExchangeServiceBinding"&gt;
            &lt;soap:address location="http://schemas.xmlsoap.org/wsdl/soap/"/&gt;
        &lt;/wsdl:port&gt;
    &lt;/wsdl:service&gt;
&lt;/wsdl:definitions&gt;</pre>
<p>Where I made up the name &#8220;ExchangeService&#8221;, an I got the names for port and binding from the lines:</p>
<pre>   &lt;wsdl:portType name="ExchangeServicePortType"&gt;</pre>
<p>and</p>
<pre>   &lt;wsdl:binding name="ExchangeServiceBinding" type="tns:ExchangeServicePortType"&gt;</pre>
<p>(On my first try I forgot the &#8220;wsdl:&#8221;-namespace in front of the port so I got the following error:</p>
<p>parsing WSDL&#8230;</p>
<p>Exception in thread &#8220;main&#8221; com.sun.tools.internal.ws.util.WSDLParseException: Encountered error in wsdl. Check namespace of element &lt;port&gt;</p>
<p>Now the parsing worked a little further and I got to the point where I need the file</p>
<pre>parsing WSDL...
[ERROR] C:\cwd\messages.xsd (Das System kann die angegebene Datei nicht finden)

[WARNING] schema_reference.4: Failed to read schema document 'messages.xsd', because 1) could not find the document; 2) the document could not be read; 3) the root element of the document is not &lt;xsd:schema&gt;.  line 5 of file:/C:/crw/modified.Services.wsdl.xml#types?schema1</pre>
<p>So I had to download all the files Henning Malzahn listed in his posting: : Services.wsdl, messages.xsd and types.xsd</p>
<p>Those files are located in the same directory on your exchange server as the wsdl. In my case:</p>
<pre>https://exchange.myuniversity.edu/EWS/messages.xsd</pre>
<p>Running wsimport now got me the new errors:</p>
<pre>parsing WSDL...
[WARNING] src-resolve: Cannot resolve the name 'xml:lang' to a(n) 'attribute declaration' component.
  line 3921 of file:/C:/cwd/types.xsd
[WARNING] s4s-elt-invalid-content.1: The content of 'ReplyBody' is invalid.  Element 'attribute' is invalid, misplaced, or occurs too often.
  line 3921 of file:/C:/cwd/types.xsd
[ERROR] undefined attribute 'xml:lang'  line 3921 of file:/C:/cwd/types.xsd</pre>
<p>Those errors all reference some line in types.xsd. As the line had a &#8220;use=\&#8221;optional\&#8221;" attribute, I thought I could just comment it out. So I had the following:</p>
<p>&lt;xs:complexType name=&#8221;ReplyBody&#8221;&gt;<br />
&lt;xs:sequence&gt;<br />
&lt;xs:element minOccurs=&#8221;0&#8243; maxOccurs=&#8221;1&#8243; name=&#8221;Message&#8221; type=&#8221;xs:string&#8221;/&gt;<br />
&lt;/xs:sequence&gt;<br />
&lt;!&#8211;    &lt;xs:attribute ref=&#8221;xml:lang&#8221; use=&#8221;optional&#8221;/&gt;&#8211;&gt;<br />
&lt;/xs:complexType&gt;</p>
<p>All these changes resulted in compiling code:</p>
<p>parsing WSDL&#8230;</p>
<p>generating code&#8230;</p>
<p>compiling code&#8230;</p>
<p>Note: C:\cwd\.\com\<br />
microsoft\schemas\exchange\services\_2006\messages\ObjectFactory.java uses unche<br />
cked or unsafe operations.<br />
Note: Recompile with -Xlint:unchecked for details.</p>
<p>Now I had to check whether I could use the Web Service features from within Java and I wasn&#8217;t too sure about it because I had come across a posting by cheeso on <a title="Connecting to Exchange using JAX-WS, part 1 - All About Interop - Site Home - MSDN Blogs" href="http://blogs.msdn.com/b/dotnetinterop/archive/2008/07/29/connecting-to-exchange-using-jax-ws-part-1.aspx">Connecting to Exchange using JAX-WS, part 1 &#8211; All About Interop &#8211; Site Home &#8211; MSDN Blogs</a> where he lists these things he had to do before he was able to use the Web Service:</p>
<p><span style="font-size:x-small;"><span style="font-size:x-small;">Let me summarize what I did to get Java to talk to Exchange:</span></span></p>
<ul>
<li>Modified the exchange.wsdl to include a service definition, and to remove all occurrences of impersonation, S2SAuth, and MailboxCulture from each wsdl:message.</li>
<li>Modified the types.xsd to eliminate the ref=&#8221;t:Path&#8221;, and replace it with actual elements</li>
<li>Use Fiddler2 to trace and debug the SOAP messages.</li>
</ul>
<p>I forgot to add the<em> -keep</em> option to my wsimport statement. I added it in order to get coding help from eclipse.</p>
<p>At this point I stopped trying for now. What I did was trying to use the amazon web service but it then I read that amazon&#8217;s webservice based on soap is not compatible with JAX-WS and that one should use JAX-RPC. Now I wonder whether exchange is compatible.</p>
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			<media:title type="html">gbideas</media:title>
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		<title>Android ViewMap example &#8211; a beginner&#8217;s very basic observations</title>
		<link>http://gbideas.wordpress.com/2011/04/09/android-viewmap-example-a-beginners-very-basic-insights/</link>
		<comments>http://gbideas.wordpress.com/2011/04/09/android-viewmap-example-a-beginners-very-basic-insights/#comments</comments>
		<pubDate>Sat, 09 Apr 2011 14:29:21 +0000</pubDate>
		<dc:creator>gbideas</dc:creator>
				<category><![CDATA[Uncategorized]]></category>

		<guid isPermaLink="false">http://gbideas.wordpress.com/?p=236</guid>
		<description><![CDATA[Hi, I&#8217;m just got an eclipse project containing code coming from http://developer.android.com/guide/tutorials/views/hello-mapview.html but with slight changes. I wanted to run it here to help with debugging some problems. As I had never written an android project I had some very basic &#8220;insights&#8221;. I had to generate my own MapKey. I got the information for that from: http://code.google.com/intl/de-DE/android/add-ons/google-apis/mapkey.html [...]<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=gbideas.wordpress.com&amp;blog=7643295&amp;post=236&amp;subd=gbideas&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>Hi,</p>
<p>I&#8217;m just got an eclipse project containing code coming from <a href="http://developer.android.com/guide/tutorials/views/hello-mapview.html">http://developer.android.com/guide/tutorials/views/hello-mapview.html</a> but with slight changes. I wanted to run it here to help with debugging some problems. As I had never written an android project I had some very basic &#8220;insights&#8221;.</p>
<ul>
<li>I had to generate my own MapKey. I got the information for that from: <a href="http://code.google.com/intl/de-DE/android/add-ons/google-apis/mapkey.html">http://code.google.com/intl/de-DE/android/add-ons/google-apis/mapkey.html</a> . For now I only got a MapKey for my  debug.keystore . You need keytool for it and it&#8217;s part of the Oracle SDK within the bin folder</li>
<li>Sometimes I might have executed the main.xml that produced an main.out.xml. I had to delete that, when it was there.</li>
<li>I wanted to have a look at the main.xml. It was not perfectly formatted. As I wasn&#8217;t sure whether it was correct on an XML-level I ran Source/Format on it. Then I was able to see that it was actually correct.</li>
<li>I had an error symbol on my project and I could run it. There were, however, no errors indicated in the log. So I ran Project/Clean and it got rid of the problem. (From: <a href="http://stackoverflow.com/questions/3638660/undefined-error-when-trying-to-run-android-tutorial-form-stuff">http://stackoverflow.com/questions/3638660/undefined-error-when-trying-to-run-android-tutorial-form-stuff</a> )</li>
<li>Then I had the error log: No command output when running: &#8216;am start -n google.map/google.map.HelloViewMap -a android.intent.action.MAIN -c android.intent.category.LAUNCHER&#8217; on device emulator&#8221; specifically</li>
</ul>
<p><span style="font-family:Consolas, Monaco, 'Courier New', Courier, monospace;font-size:12px;line-height:18px;white-space:pre;">eclipse.buildId=M20100909-0800java.version=1.6.0_24java.vendor=Sun Microsystems Inc.BootLoader constants: OS=win32, ARCH=x86, WS=win32, NL=de_DEFramework arguments:  -product org.eclipse.epp.package.jee.productCommand-line arguments:  -os win32 -ws win32 -arch x86 -product org.eclipse.epp.package.jee.product</span></p>
<pre>ErrorSat Apr 09 15:56:54 CEST 2011No command output when running: 'am start -n google.map/google.map.HelloViewMap -a android.intent.action.MAIN -c android.intent.category.LAUNCHER' on device emulator-5554
com.android.ddmlib.ShellCommandUnresponsiveException	at com.android.ddmlib.AdbHelper.executeRemoteCommand(AdbHelper.java:408)	at com.android.ddmlib.Device.executeShellCommand(Device.java:276)	at com.android.ide.eclipse.adt.internal.launch.ActivityLaunchAction.doLaunchAction(Unknown Source)	at com.android.ide.eclipse.adt.internal.launch.AndroidLaunchController.launchApp(Unknown Source)	at com.android.ide.eclipse.adt.internal.launch.AndroidLaunchController.clientChanged(Unknown Source)	at com.android.ddmlib.AndroidDebugBridge.clientChanged(AndroidDebugBridge.java:867)	at com.android.ddmlib.Device.update(Device.java:398)	at com.android.ddmlib.Client.update(Client.java:834)	at com.android.ddmlib.HandleAppName.handleAPNM(HandleAppName.java:90)	at com.android.ddmlib.HandleAppName.handleChunk(HandleAppName.java:64)	at com.android.ddmlib.MonitorThread.callHandler(MonitorThread.java:414)	at com.android.ddmlib.MonitorThread.processClientActivity(MonitorThread.java:322)	at com.android.ddmlib.MonitorThread.run(MonitorThread.java:263)
<span style="font-family:Georgia, 'Times New Roman', 'Bitstream Charter', Times, serif;font-size:13px;line-height:19px;white-space:normal;">
</span></pre>
<p><span style="font-family:Georgia, 'Times New Roman', 'Bitstream Charter', Times, serif;font-size:13px;line-height:19px;white-space:normal;"> </span><span style="font-family:Georgia, 'Times New Roman', 'Bitstream Charter', Times, serif;font-size:13px;line-height:19px;white-space:normal;"> .  <a href="http://www.anddev.org/sdk-adt-emulator-problems-f16/unparsed-aapt-errors-check-the-console-for-output-t12615.html">http://www.anddev.org/sdk-adt-emulator-problems-f16/unparsed-aapt-errors-check-the-console-for-output-t12615.html</a> told me to just delete it or clean the project.</span></p>
<ul>
<li>I started the Android app but I wasn&#8217;t sure whether it was still running when I hit the &#8220;Home&#8221; button to go back to the main menu. I found the taskmanager at &#8220;All Programs/DevTools/Running Processes&#8221;. it seems, it was not running after I went back to the main menu.</li>
<li>I tried to do some logging with System.out.println but <a href="http://developer.android.com/resources/faq/commontasks.html#logging">http://developer.android.com/resources/faq/commontasks.html#logging</a><a href="http://groups.google.com/group/android-developers/browse_thread/thread/a4896b24bd355a30/208a143b4eec58c0?lnk=gst&amp;q=System.out.println&amp;pli=1">http://groups.google.com/group/android-developers/browse_thread/thread/a4896b24bd355a30/208a143b4eec58c0?lnk=gst&amp;q=System.out.println&amp;pli=1</a> and <a href="http://developer.android.com/reference/android/util/Log.html">http://developer.android.com/reference/android/util/Log.html</a> tell me to use Log.v(&#8220;myAppTag&#8221;, &#8220;step 5 is about to happen&#8221;) instead. You can read the output with starting ddms.bat from &#8220;android-sdk-windows/tools&#8221;. But System.out.println is also listed within Dalvik Debug Monitor. You will have to click on the emulator in the upper left windows to see the outputs.</li>
<li>I came across the bug:  <a href="http://code.google.com/p/android/issues/detail?id=8816">http://code.google.com/p/android/issues/detail?id=8816</a> that Geocoder.getFromLocationName throws an java.io.IOException: Service not Available. This seems to be a bug in the 2.2 emulator. In the bug link there is comment #21 with a workaround. I downgraded to 2.1 (my device is 2.1 anyhow). However then in main.xml I had to replace all &#8220;match_parent&#8221; by &#8220;fill_parent&#8221;. Tihs page <a href="http://stackoverflow.com/questions/4936553/android-how-can-you-align-a-button-at-the-bottom-and-listview-above">http://stackoverflow.com/questions/4936553/android-how-can-you-align-a-button-at-the-bottom-and-listview-above</a> says that match_parent was fill_parent till 2.1.</li>
<li>You can set the information the android emulator sends to the android operating systems. <a href="http://www.helloandroid.com/tutorials/how-set-location-emulator">http://www.helloandroid.com/tutorials/how-set-location-emulator</a> tells you, you can do it in ddms.bat (Dalvik Debug Monitor) in the tab &#8220;Emulator Control&#8221; under Location Controls.</li>
<li>One should maybe put the geocoder information request in a separate thread as it needs an internet connection that might be slow. <a href="http://stackoverflow.com/questions/472313/android-reverse-geocoding-getfromlocation">http://stackoverflow.com/questions/472313/android-reverse-geocoding-getfromlocation</a></li>
<li>I got this error message <em>ERROR/AndroidRuntime(331): Uncaught handler: thread main exiting due to uncaught exception 06-14 22:13:34.031: ERROR/AndroidRuntime(331): java.lang.RuntimeException: Unable to start activity ComponentInfo{com.example/com.example.HelloMap}:</em> when I tried to add a map to an Activity. As pointed out here: <a href="http://stackoverflow.com/questions/3040307/android-hellomap-example-giving-exception">http://stackoverflow.com/questions/3040307/android-hellomap-example-giving-exception</a> I had to extend my Activity from MapActivity. In order for that to be possible I had to change the Android I compile against from 1.5 to &#8220;Google API + Android 1.5&#8243;. For that to work I had to let Eclipse add the required &#8220;isRouteDisplayed()&#8221; method.</li>
<li>Then I got the error java.lang.NoClassDefFoundError: &#8230; and then the name of the class I had just changed from extending not Activity but MapActivity. I forgot adding &#8217;&lt;uses-library android:name=&#8221;com.google.android.maps&#8221; /&gt;&#8217; in the manifest.xml.</li>
<li>I&#8217;m now using a &#8220;clickable = true&#8221; map within a scrollable Activity. Now only the horizontal touch-movements are represented in the map. When I flick up and down this is only reflected in moving the whole activity up and down but not the map. Is there a UI trick for the user to use the map completely?</li>
<li></li>
</ul>
<p>I&#8217;ll publish this now and might come back later</p>
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		<title>VLC increase volume over 200%</title>
		<link>http://gbideas.wordpress.com/2011/02/17/vlc-increase-volume-over-200/</link>
		<comments>http://gbideas.wordpress.com/2011/02/17/vlc-increase-volume-over-200/#comments</comments>
		<pubDate>Thu, 17 Feb 2011 23:22:16 +0000</pubDate>
		<dc:creator>gbideas</dc:creator>
				<category><![CDATA[software]]></category>
		<category><![CDATA[amplifier]]></category>
		<category><![CDATA[audio]]></category>
		<category><![CDATA[increase]]></category>
		<category><![CDATA[increase volume]]></category>
		<category><![CDATA[preamplifier]]></category>
		<category><![CDATA[setting]]></category>
		<category><![CDATA[settings]]></category>
		<category><![CDATA[soft]]></category>
		<category><![CDATA[sound]]></category>
		<category><![CDATA[VLC]]></category>
		<category><![CDATA[volume]]></category>

		<guid isPermaLink="false">http://gbideas.wordpress.com/?p=231</guid>
		<description><![CDATA[How to increase the volume in VLC over the max setting of 200%: Click in the video and use the scrollwheel to get up to 400% volume.
Additionally: Open the amplifier and set the preamplifier to 20dB.<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=gbideas.wordpress.com&amp;blog=7643295&amp;post=231&amp;subd=gbideas&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>I want to raise the volume in VLC over 200%.</p>
<p>I have a video file with very low volume on the audio track. I want to play this specific file with increased volume.</p>
<p>I found a solution <a title="Increase Volume Tremendously in VLC Media Player" href="http://www.bestpctips.com/increase-volume-on-your-computer-tremendously-using-vlc-media-player/">bestpctips.com</a>. They suggest:</p>
<p><strong>Click in the video and use the scroll wheel of your mouse to increase the volume to up to 400%.</strong></p>
<p>And to increase it further you can use this small workaround of which I though earlier:</p>
<p>Start the equalizer via a button or via &#8220;Tools&#8221;/&#8221;Effects and Filters&#8221;. Set the preamplifier to 20dB. (it&#8217;s the first bar) Activate the graphic equalizer. Set the volume to 200%.</p>
<p>It&#8217;s not the perfect solution. And maybe you can make it even better if you increase the max amplifier setting of 20dB to a high value in the settings. But at least its an easy to activate work-around.</p>
<p>Please comment if you know how to get rid of the 400% maximum.</p>
<p>Later on I found the tip also on <a title="VLC: increase the volume to 400%" href="http://en.kioskea.net/faq/5618-vlc-increase-the-volume-to-400">kioskea.net</a>. <a title="VLC Player Tricks : Increase the Volume to 400%" href="http://nuvvenuvve.blogspot.com/2007/07/vlc-player-tricks-increase-volume-to.html">Nuvvenuvve</a> knows you can also use CTRL + UP-Arrow for increasing the volume past the factor 2.</p>
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		<title>No video calls on iPhone 3G with skype app 3.0.0 (Not even one-way)</title>
		<link>http://gbideas.wordpress.com/2010/12/31/no-video-calls-on-iphone-3g-with-skype-app-3-0-0-not-even-one-way/</link>
		<comments>http://gbideas.wordpress.com/2010/12/31/no-video-calls-on-iphone-3g-with-skype-app-3-0-0-not-even-one-way/#comments</comments>
		<pubDate>Fri, 31 Dec 2010 11:57:25 +0000</pubDate>
		<dc:creator>gbideas</dc:creator>
				<category><![CDATA[iOS]]></category>
		<category><![CDATA[iPhone 3G]]></category>
		<category><![CDATA[iPod Touch]]></category>
		<category><![CDATA[mobile phone]]></category>
		<category><![CDATA[software]]></category>
		<category><![CDATA[streaming media]]></category>
		<category><![CDATA[broken]]></category>
		<category><![CDATA[broken by design]]></category>
		<category><![CDATA[iPhone]]></category>
		<category><![CDATA[iPhone App]]></category>
		<category><![CDATA[not working]]></category>
		<category><![CDATA[one-way]]></category>
		<category><![CDATA[skype]]></category>
		<category><![CDATA[two-way]]></category>
		<category><![CDATA[video]]></category>
		<category><![CDATA[video calls]]></category>
		<category><![CDATA[video stream]]></category>

		<guid isPermaLink="false">http://gbideas.wordpress.com/?p=226</guid>
		<description><![CDATA[When calling an iPhone 3G with the new Skype app 3.0 you can not establish a two-way or even one-way video chat. I tried it.<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=gbideas.wordpress.com&amp;blog=7643295&amp;post=226&amp;subd=gbideas&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>Everyone is reporting on the new Skype iPhone / iOS app. (<a href="http://www.welt.de/print/welt_kompakt/webwelt/article11911295/Neue-Skype-Software-fuer-das-iPhone.html">Welt</a> <a href="http://www.macnews.de/news/68001/iphone-skype-3-0-unterstutzt-video-chats-uber-wlan-und-umts/">MacNews</a> <a href="http://www.golem.de/1012/80388.html">Golem</a> <a href="http://www.heise.de/mac-and-i/meldung/Skype-fuer-iOS-beherrscht-Videotelefonie-1161897.html">Heise</a> <a href="http://blogs.skype.com/en/2010/12/iphone_video_calls.html">Skype blog</a> <a href="http://www.9to5mac.com/45073/skype-for-iphone-gets-video-chat-works-over-3g-and-with-macs">9to5Mac</a> <a href="http://www.engadget.com/2010/12/30/skype-video-calling-for-iphone-is-official-available-today/">Engadget</a>)</p>
<p>Everyone says: There are two-way video calls from camera equipped iOS devices to other skype video enabled devices (like PCs with their desktop application or other iPhone 3GS and iPhone 4). They also say that you can receive a video stream on an iPad and an iTouch 3G.</p>
<p>They don&#8217;t state (explicitly) that the iPhone 3G lacks the capability to receive and display a video stream.</p>
<p>So I went ahead and called my iPhone 3G from a computer with a webcam (current desktop skype). The button to start a video chat was activated when looking at my iPhone-Skype-contact, so I clicked it.  However, the Skype app never finished starting the video feed. (Usually the video stream comes up within a video seconds.) app version 3.0.0 / firmware: 4.2.1 .</p>
<p>So I conclude:</p>
<p>Can the iPhone 3G do video calls with the new Skype app?</p>
<p>There are no video calls with the new Skype App 3.0 on the iPhone 3G.</p>
<p>You cannot receive a video stream with the iPhone 3G. You cannot establish a one-way video call with the iPhone 3G. (You wouldn&#8217;t expect 2-way videocalls anyway as the iPhone 3G doesn&#8217;t support video recording with the standard firmware.)</p>
<p>Maybe someday jailbroken iPhones can wrap the Skype app so it will allow receiving video calls.</p>
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		<title>Adding temporary notes to LaTeX draft compiles</title>
		<link>http://gbideas.wordpress.com/2010/04/13/adding-temporary-notes-to-latex-draft-compiles/</link>
		<comments>http://gbideas.wordpress.com/2010/04/13/adding-temporary-notes-to-latex-draft-compiles/#comments</comments>
		<pubDate>Tue, 13 Apr 2010 09:02:48 +0000</pubDate>
		<dc:creator>gbideas</dc:creator>
				<category><![CDATA[LaTeX]]></category>
		<category><![CDATA[software]]></category>

		<guid isPermaLink="false">http://gbideas.wordpress.com/?p=218</guid>
		<description><![CDATA[This is a short example code for comments in LaTeX draft documents. Depending on a variable at the start of the LaTeX document the comments are either compiled into the .pdf or .dvi file or they are kept out of it.<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=gbideas.wordpress.com&amp;blog=7643295&amp;post=218&amp;subd=gbideas&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>Suppose you do a LaTeX document, and you want to take notes within the compiled document that should be visible in the drafts but not in the final document.</p>
<p>Here is one way of doing it (but it messes with the page layout as it puts the comments in the document itself instead of at the border):</p>
<p><code><br />
\usepackage{ifthen}<br />
\usepackage{color}<br />
\newboolean{FinalVersionWithoutNotes}<br />
\newcommand{\NNF}[1]{\ifthenelse{\boolean{FinalVersionWithoutNotes}}{}{\colorbox{yellow}{#1}}}<br />
\setboolean{FinalVersionWithoutNotes}{false}<br />
</code></p>
<p>And within the document you write:<br />
<code>In group theory the left inverse is sometimes equal to the right inverse \NNF{Remember to add a proof of this statement and delete the "someimes" as soon as your done.}, therefore ....</code></p>
<p>This will just paste the text within the NNF (Notes Non Final) command into the document in a yellow box (that doesn&#8217;t care about linebreaks at the end of the line). If you change the boolean:</p>
<p><code> \setboolean{FinalVersionWithoutNotes}{true}<br />
</code></p>
<p>non of the stuff in the NNF command will be compiled in the document.</p>
<p>Comments:</p>
<ul>
<li>There are no line-breaks or no spaces allowed in the <em>newcommand</em> passage.</li>
<li>If you have a special include-file for all your commands you can put everything from the first block in there. But I guess it makes sense to put the &#8220;\setboolean{FinalVersionWithoutNotes}{false}&#8221; within your document itself as you want to change this variable regularly.</li>
<li>It would be better if the box supported line breaks.</li>
<li>It would be even better if the box wasn&#8217;t placed in the document text but to the side of it. In the current version the layout of your documents changes as the amount of flow text changes. So you&#8217;ll have to do the layout with the <em>FinalVersionWithoutNotes </em>boolean set to <em>true</em>.</li>
</ul>
<p>Thanks for <a href="http://de.wikibooks.org/wiki/LaTeX-W%C3%B6rterbuch:_textcolor">LaTeX-Wörterbuch: textcolor</a> and <a href="http://zyliu2005.blogspot.com/2007/06/latex-how-to-use-conditional.html">Sunlife: Latex: how to use conditional compilation</a> for the information.</p>
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		<title>Use SpeedStep to Minimize Fan Noise even while laptop is plugged in &#8211; via Win XP command line</title>
		<link>http://gbideas.wordpress.com/2010/02/04/use-speedstep-to-minimize-fan-noise-even-while-laptop-is-plugged-in-via-win-xp-command-line/</link>
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		<pubDate>Thu, 04 Feb 2010 22:36:19 +0000</pubDate>
		<dc:creator>gbideas</dc:creator>
				<category><![CDATA[hardware]]></category>
		<category><![CDATA[software]]></category>
		<category><![CDATA[WinXP]]></category>
		<category><![CDATA[command line]]></category>
		<category><![CDATA[commandline]]></category>
		<category><![CDATA[control panel]]></category>
		<category><![CDATA[CPU]]></category>
		<category><![CDATA[Energieoptionen]]></category>
		<category><![CDATA[fan]]></category>
		<category><![CDATA[Intel]]></category>
		<category><![CDATA[noise]]></category>
		<category><![CDATA[Pentium M]]></category>
		<category><![CDATA[power scheme]]></category>
		<category><![CDATA[powercfg.cpl]]></category>
		<category><![CDATA[powercfg.exe]]></category>
		<category><![CDATA[slower]]></category>
		<category><![CDATA[SpeedStep]]></category>
		<category><![CDATA[throttle]]></category>

		<guid isPermaLink="false">http://gbideas.wordpress.com/?p=205</guid>
		<description><![CDATA[If you want to throttle your CPU via SpeedStep even while plugged in, you need to change a power scheme. You can add a new from the Power Options dialog ("control powercfg.cpl") and change the SpeedStep behaviour while on AC via "POWERCFG.EXE /CHANGE MyPowerConfig1LowCPUSpeed /processor-throttle-ac CONSTANT". This will slower the CPU so the fan won't go on.<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=gbideas.wordpress.com&amp;blog=7643295&amp;post=205&amp;subd=gbideas&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>If you want to save battery time or want to lower the fan noise in Win XP you can change the power settings. However non of the predefined power schemes uses low CPU speed while plugged in. Here is how you add such a profile:</p>
<p>&#8212; short version of the post &#8212;</p>
<p>Start a command-line as Administrator Privileges (for example via <a href="http://www.heise.de/ct/ftp/05/23/112/">MachMichAdmin</a>) and then do:</p>
<p>&emsp;&emsp;&emsp;REM List current energy profiles<br />
<code>POWERCFG /LIST</code><br />
&emsp;&emsp;&emsp;REM copy current profile with new name &#8216;LessFanProfile&#8217;<br />
<code>POWERCFG /CREATE LessFanProfile</code><br />
&emsp;&emsp;&emsp;REM change profile &#8216;LessFanProfile&#8217; to use lower CPU speed all the time<br />
<code>POWERCFG /CHANGE LessFanProfile /processor-throttle-ac CONSTANT</code><br />
<code>POWERCFG /CHANGE LessFanProfile /processor-throttle-dc CONSTANT</code><br />
&emsp;&emsp;&emsp;REM activate &#8216;LessFanProfile&#8217;<br />
<code>POWERCFG /SETACTIVCE LessFanProfile</code></p>
<p>optionally you can do:</p>
<p>&emsp;&emsp;&emsp;REM List profiles, note the new addition<br />
<code>POWERCFG /LIST</code></p>
<p>and</p>
<p>&emsp;&emsp;&emsp;REM Get a list of all properties of the profiles &#8216;LessFanProfile&#8217;<br />
<code>POWERCFG /QUERY LessFanProfile</code></p>
<p>&#8212; long version of the post &#8212;</p>
<p>You can open the power setting dialog by calling</p>
<p><code>CONTROL POWERCFG.CPL</code></p>
<p>from the command line. (You might want to start this via command line, because you might want to work with a restricted user account. Then you can call MachMichAdmin [it's a <em>WinXP sudo</em> offered by Germany's publisher of the most professional computer information magazines. <a href="http://www.heise.de/software/download/machmichadmin/31780">MachMichAdmin German Page in their Software Directory</a>. The link to the <a href="http://www.heise.de/ct/ftp/05/23/112/">MachMichAdmin info page (German).</a> The direct link to the <a href="ftp://ftp.heise.de/pub/ct/listings/0523-112.zip">zip file of the MachMichAdmin batch files</a>.] to get a shell with Admin privileges under your username. And from there you can call the dialog with Admin rights.)</p>
<p>However, it turns out that non of the profiles you find there enforces a lower CPU speed while the laptop is plugged in.</p>
<p>You can head over to <a href="http://www.orthogonalthought.com/blog/index.php/2007/09/intel-speedstep-windows-xp-and-confusing-power-profiles/">Orthogonal Thought: Intel SpeedStep, Windows XP, and confusing Power Profiles</a> and read what profiles does what. If you want a profile that throttles the CPU all the time, do the following:</p>
<p>Start the powercfg.cpl with Admin rights (in German: Energieoptionen)</p>
<p>Add another energy profile: you do this by clicking on &#8220;Save As&#8221;. This will copy the chosen Energy scheme, with the adjustments you made. I assume you choose the name &#8220;MyPowerConfig1LowCPUSpeed&#8221; for your profile after clicking &#8220;Save As&#8221; (but anything else will do). [You can see <a href="http://www.lancelhoff.com/adjust-windows-xp-power-options/">a picture of the Power Options Properties dialog in this blog post.</a>]</p>
<p>Then go to a command line and try:</p>
<p><code>POWERCFG.EXE /LIST</code></p>
<p>This will give you a list of your power schemes. &#8220;MyPowerConfig1LowCPUSpeed&#8221; should be one of them.</p>
<p>You can look at your new energy profile with</p>
<p><code>POWERCFG.EXE /QUERY MyPowerConfig1</code>LowCPUSpeed</p>
<address><em>Then change the behaviour while on AC (plugged in) regarding SpeedStep by doing the following with Admin privileges (at least for Intel processors with SpeedStep)</em><br />
</address>
<p><code>POWERCFG.EXE /CHANGE MyPowerConfig1</code>LowCPUSpeed<code> /processor-throttle-ac CONSTANT</code></p>
<p>You can also change the behaviour while on battery by the following command:</p>
<p><code>POWERCFG.EXE /CHANGE MyPowerConfig1</code>LowCPUSpeed<code> /processor-throttle-dc CONSTANT</code></p>
<p>The keywords are CONSTANT = &#8220;CPU(s) run in lowest performance state&#8221;, ADAPTIVE = &#8220;adapts to CPU usage&#8221;, NONE = &#8220;CPU(s) run in highest performance state&#8221; (and there is a fourth keyword but it&#8217;s of no use) [Thanks again to <a href="http://www.orthogonalthought.com/blog/index.php/2007/09/intel-speedstep-windows-xp-and-confusing-power-profiles/">Orthogonal Thought: Intel SpeedStep, Windows XP, and confusing Power Profiles</a> for the information, go there to read it much better.]</p>
<p>You can now activate this profile from the Power Options dialog (run CONTROL POWERCFG.CPL) by choosing it from the drop down menu and pressing okay. I find this useful for the nights I want my computer to run but be very, very silent. When I activate this option, the fan won&#8217;t run at all, and I can sleep tight within the same room, even though the laptop (with the screen turned off) calculates some stuff (albeit slowly).</p>
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		<title>Thunderbird 3 collapse header info as in v2 via Add-On</title>
		<link>http://gbideas.wordpress.com/2010/01/31/thunderbird-3-collapse-header-info-as-in-v2/</link>
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		<pubDate>Sun, 31 Jan 2010 22:42:45 +0000</pubDate>
		<dc:creator>gbideas</dc:creator>
				<category><![CDATA[software]]></category>
		<category><![CDATA[Add-On]]></category>
		<category><![CDATA[Addon]]></category>
		<category><![CDATA[feature]]></category>
		<category><![CDATA[GUI]]></category>
		<category><![CDATA[Thunderbird]]></category>

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		<description><![CDATA[Thunderbird 3.0 doesn't support compact headers but always shows the expanded version of the header information. You can change this behaviour and collapse the information via the Thunderbird Add-On CompactHeader<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=gbideas.wordpress.com&amp;blog=7643295&amp;post=198&amp;subd=gbideas&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>I installed Thunderbird 3.0 lately and now I switched to 3.0.1. Unfortunately both versions lack the capability to collapse the information from the header of the mail. I have no read this blog post: <a href="http://weblogs.mozillazine.org/dmose/archives/2009/06/thunderbird_compact_header_mov.html">Mozillazine.org :  dmose Thunderbird Compact Header</a> It states that &#8220;compact headers&#8221; was taken out of the core Thunderbird functionality set in order to focus on other tasks within the development. But there is a Thunderbird Add-On called CompactHeader which recreates the old behaviour (and more I guess).<br />
So if you want to get your compact headers back instead of living with the expanded header info, head over to<a href="https://addons.mozilla.org/thunderbird/addon/13564"> addons.mozilla.org : Thunderbird &#8211; CompactHeader</a> and try it. I can&#8217;t guarantee for the software but at the first glance it looked like the add-on I was searching for. (I use version 1.1.5 right now)</p>
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		<title>Integralkerne in L.W. Kantorowitsch, G. P. Akilow Funktionalanalysis in normierten Räumen</title>
		<link>http://gbideas.wordpress.com/2010/01/23/integralkerne-in-l-w-kantorowitsch-g-p-akilow-funktionalanalysis-in-normierten-raumen/</link>
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		<pubDate>Sat, 23 Jan 2010 13:13:46 +0000</pubDate>
		<dc:creator>gbideas</dc:creator>
				<category><![CDATA[book]]></category>
		<category><![CDATA[math]]></category>
		<category><![CDATA[Akilow]]></category>
		<category><![CDATA[bounded operators]]></category>
		<category><![CDATA[functional analysis]]></category>
		<category><![CDATA[Funktionalanalysis]]></category>
		<category><![CDATA[integral kernel]]></category>
		<category><![CDATA[integral operators]]></category>
		<category><![CDATA[ISBN:3871443271]]></category>
		<category><![CDATA[Kantorowitsch]]></category>
		<category><![CDATA[kernel]]></category>
		<category><![CDATA[linear operators]]></category>
		<category><![CDATA[MR177273]]></category>
		<category><![CDATA[normed spaces]]></category>
		<category><![CDATA[normierte Räume]]></category>
		<category><![CDATA[normierte Vektorräume]]></category>
		<category><![CDATA[operators]]></category>
		<category><![CDATA[Schwartz kernel]]></category>
		<category><![CDATA[stetiger Integralkern]]></category>

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		<description><![CDATA[These are German annotations to the book L.W. Kantorowitsch, G. P. Akilow Funktionalanalysis in normierten Räumen (German translation). I list all occurrences of integral kernels. Those are functions like the Schwartz kernel. Unfortunately the book only contains theorems that yield properties of the operator from properties known about the kernel. For example in all most all cases the kernel k is supposed to be continuous and mostly the domains used are compact, mostly just intervals [a,b].<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=gbideas.wordpress.com&amp;blog=7643295&amp;post=115&amp;subd=gbideas&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>My blog was supposed to be english only. But I started compromising on the intent in blog post #2, so I figured I might as well compromise regarding the used language. Someday I should start blogs sorted by topic and language.</p>
<p>I&#8217;m in search for a theorem stating the existence and smoothness properties of an integral kernel function.</p>
<p>I haven&#8217;t found many resources regarding this, but I was told to look at <strong>L.W. Kantorowitsch, G. P. Akilow Funktionalanalysis in normierten Räumen</strong>, ISBN: 3 87144 327 1, which is a translation of their Russian book into German by Heinz Langer and Rolf Kühne<strong>.</strong> I couldn&#8217;t find any theorems in there that I needed (I want to proof the existence of a smooth kernel function for a square of any smoothing operator.) But as I&#8217;ve scanned through the book now, I want to list what my comment were. Actually it&#8217;s just a list of all mentionings of integral operators. I don&#8217;t know whether this is of use for anyone, but maybe someone down the road has the same question, gets told to read the same book, so maybe this will save him or her some time. [And by writing this down, I know I've really read the book <img src='http://s1.wp.com/wp-includes/images/smilies/icon_wink.gif' alt=';-)' class='wp-smiley' />  ]<br />
As the book is in German, I will write this blog post in German:</p>
<p>Dies ist eine Zusammenstellung aller Erwähnungen von Integralkernen in <strong>L.W. Kantorowitsch, G. P. Akilow <em>Funktionalanalysis in normierten Räumen</em></strong> übersetzt ins deutsche von Heinz Langer und Rolf Kühne. Hier ist z.B. der <a title="Open Library:  	Funktionalanalysis in normierten Räumen [von] L.W. Kantorowitsch [und] G.P. Akilow" href="http://openlibrary.org/b/OL16521594M/Funktionalanalysis_in_normierten_R%C3%A4umen_von_L.W._Kantorowitsch_und_G.P._Akilow.">OpenLibrary Artikel zu Funktionalanalysis in normierten Räumen</a>. Es erschien in Mathematische Lehrbücher und Monographien &#8212; Bd. 17 und das Erscheinungsjahr war 1964 beim Akademie-Verlag Berlin. Mathematical Reviews (MathSciNet):          <a href="http://www.ams.org/mathscinet-getitem?mr=177273">MR177273</a>. Hier der Datensatz in der <a title="DNB: Funktionalanalysis in normierten Räumen" href="http://d-nb.info/452309328">Deutschen National Bibliothek DNB: Funktionalanalysis in normierten Räumen</a>. Das russische Original läuft unter: {\cyr Funktsional<tt>ʹ</tt>nyĭ analiz v normirovannykh  prostranstvakh} auf der Seite von <a href="http://www.ams.org/mathscinet/pdf/119071.pdf?pg1=MR&amp;r=1&amp;s1=119071">MR zum russischen Original findet sich auch der russische Name</a>. ISBN: 3871443271</p>
<p>Zuerst zur Notation: Ich brauchte mehrmals Erinnerung bzgl. der Notation. Und zwar steht das <strong>C</strong> im Buch für <img src='http://s0.wp.com/latex.php?latex=C%5E0%28%5Ba%2Cb%5D%2C%5Cmathbb%7BR%7D%29&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='C^0([a,b],&#92;mathbb{R})' title='C^0([a,b],&#92;mathbb{R})' class='latex' /> (siehe Seite 5). Das <img src='http://s0.wp.com/latex.php?latex=%5Ctilde%7BM%7D&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;tilde{M}' title='&#92;tilde{M}' class='latex' /> im Buch steht für <img src='http://s0.wp.com/latex.php?latex=L%5E%7Binfty%7D%28D%2C%5Cmathbb%7BR%7D%29&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='L^{infty}(D,&#92;mathbb{R})' title='L^{infty}(D,&#92;mathbb{R})' class='latex' /> für eine meist beschränkte, messbare Menge D. Für <img src='http://s0.wp.com/latex.php?latex=L_T%5Ep&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='L_T^p' title='L_T^p' class='latex' /> steht für <img src='http://s0.wp.com/latex.php?latex=L%5Ep%28T%2C%5Cmathbb%7BR%7D%29&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='L^p(T,&#92;mathbb{R})' title='L^p(T,&#92;mathbb{R})' class='latex' />. Und <img src='http://s0.wp.com/latex.php?latex=%5Ctext%7Bmes%7D+T&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;text{mes} T' title='&#92;text{mes} T' class='latex' /> steht für das Maß <img src='http://s0.wp.com/latex.php?latex=%5Cmu+%28T%29&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;mu (T)' title='&#92;mu (T)' class='latex' /> der Menge T. Auf Seite 100 gibt es dann die Zeile <img src='http://s0.wp.com/latex.php?latex=%28x%2Cy%29%3D%5Cint+_a%5Ebx%28t%29%5Coverline%7By%28t%29%7D+dt&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='(x,y)=&#92;int _a^bx(t)&#92;overline{y(t)} dt' title='(x,y)=&#92;int _a^bx(t)&#92;overline{y(t)} dt' class='latex' />. Hier sind Funktionen also komplex-wertig. Wie man an der Notation erkennt, welche Funktionen komplex-wertig sind und welche reell-wertig, kann ich nicht genau sagen.  Charakteristische Zahlen sind die multiplikativen Inversen der Eigenwert ungleich Null. Auf Seite 61 wird auch noch das wesentliche Supremum <img src='http://s0.wp.com/latex.php?latex=%5Ctext%7Besssup%7D&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;text{esssup}' title='&#92;text{esssup}' class='latex' /> eingeführt. Das Buch nutzt hierfür die Notation <img src='http://s0.wp.com/latex.php?latex=%5Ctext%7Bvrai+max%7D&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;text{vrai max}' title='&#92;text{vrai max}' class='latex' />. Insbesondere heißt es in der Fußnote zur Definition von &#8220;vrai max&#8221; auf Seite 61: Das wesentliche Maximum der Funktion f(t) wird vraimax f(t) bezeichnet und es ist definiert als das Infimum der Zahlen A, für welche die Menge aller Werte t mit f(t)&gt;A das Maß Null hat.</p>
<p>So nun zu den Stellen im Buch, die Integralkerne benutzen:</p>
<p><strong>S.90ff</strong> :  Für Funktionen <img src='http://s0.wp.com/latex.php?latex=C%5E0%28%5Ba%2Cb%5D%2C%5Cmathbb%7BR%7D%29&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='C^0([a,b],&#92;mathbb{R})' title='C^0([a,b],&#92;mathbb{R})' class='latex' /> und ein stetiges <img src='http://s0.wp.com/latex.php?latex=k%5Cin+C%5Eo%28%5Ba%2Cb%5D%5Ctimes+%5Ba%2Cb%5D%2C%5Cmathbb%7BR%7D%29&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='k&#92;in C^o([a,b]&#92;times [a,b],&#92;mathbb{R})' title='k&#92;in C^o([a,b]&#92;times [a,b],&#92;mathbb{R})' class='latex' /> kann man einen Integraloperator A definieren mittels <img src='http://s0.wp.com/latex.php?latex=As%28m%29+%3D+%5Cint+_%7B%5Ba%2Cb%5D%7D+k%28m%2Cn%29s%28n%29&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='As(m) = &#92;int _{[a,b]} k(m,n)s(n)' title='As(m) = &#92;int _{[a,b]} k(m,n)s(n)' class='latex' /> für eine verschiedene Funktionenen. Es wird dann gezeigt:</p>
<p><img src='http://s0.wp.com/latex.php?latex=A%3A+C%5Eo%28%5Ba%2Cb%5D%2C%5Cmathbb%7BR%7D%29+%5Cto+C%5Eo%28%5Ba%2Cb%5D%2C%5Cmathbb%7BR%7D%29&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='A: C^o([a,b],&#92;mathbb{R}) &#92;to C^o([a,b],&#92;mathbb{R})' title='A: C^o([a,b],&#92;mathbb{R}) &#92;to C^o([a,b],&#92;mathbb{R})' class='latex' /> hat die Operatornorm <img src='http://s0.wp.com/latex.php?latex=%5Ctext%7Bmax%7D_%7Bs%5Cin+%5Ba%2Cb%5D%7D%5Cint_a%5Eb%7Ck%28s%2Ct%29%7Cdt&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;text{max}_{s&#92;in [a,b]}&#92;int_a^b|k(s,t)|dt' title='&#92;text{max}_{s&#92;in [a,b]}&#92;int_a^b|k(s,t)|dt' class='latex' />.</p>
<p><img src='http://s0.wp.com/latex.php?latex=A%3A+L%5E1%28%5Ba%2Cb%5D%2C%5Cmathbb%7BR%7D%29+%5Cto+L%5E1%28%5Ba%2Cb%5D%2C%5Cmathbb%7BR%7D%29&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='A: L^1([a,b],&#92;mathbb{R}) &#92;to L^1([a,b],&#92;mathbb{R})' title='A: L^1([a,b],&#92;mathbb{R}) &#92;to L^1([a,b],&#92;mathbb{R})' class='latex' /> hat die Operatornorm <img src='http://s0.wp.com/latex.php?latex=%5Ctext%7Bmax%7D_%7Bt%5Cin+%5Ba%2Cb%5D%7D%5Cint_a%5Eb%7Ck%28s%2Ct%29%7Cds&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;text{max}_{t&#92;in [a,b]}&#92;int_a^b|k(s,t)|ds' title='&#92;text{max}_{t&#92;in [a,b]}&#92;int_a^b|k(s,t)|ds' class='latex' />.</p>
<p><img src='http://s0.wp.com/latex.php?latex=A%3A+L%5E1%28%5Ba%2Cb%5D%2C%5Cmathbb%7BR%7D%29+%5Cto+C%5Eo%28%5Ba%2Cb%5D%2C%5Cmathbb%7BR%7D%29&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='A: L^1([a,b],&#92;mathbb{R}) &#92;to C^o([a,b],&#92;mathbb{R})' title='A: L^1([a,b],&#92;mathbb{R}) &#92;to C^o([a,b],&#92;mathbb{R})' class='latex' /> hat die Operatornorm <img src='http://s0.wp.com/latex.php?latex=%5Ctext%7Bmax%7D_%7Bs%2Ct%5Cin+%5Ba%2Cb%5D%7D%7Ck%28s%2Ct%29%7C&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;text{max}_{s,t&#92;in [a,b]}|k(s,t)|' title='&#92;text{max}_{s,t&#92;in [a,b]}|k(s,t)|' class='latex' />.</p>
<p>Außerdem ist <img src='http://s0.wp.com/latex.php?latex=A%3AL%5E2%28%5Ba%2Cb%5D%2C%5Cmathbb%7BR%7D%29+%5Cto+L%5E2%28%5Ba%2Cb%5D%2C%5Cmathbb%7BR%7D%29&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='A:L^2([a,b],&#92;mathbb{R}) &#92;to L^2([a,b],&#92;mathbb{R})' title='A:L^2([a,b],&#92;mathbb{R}) &#92;to L^2([a,b],&#92;mathbb{R})' class='latex' /> definiert und stetig, falls <img src='http://s0.wp.com/latex.php?latex=%5Cint_%7B%5Ba%2Cb%5D%5E2%7D%7Ck%28s%2Ct%29%7C%5E2dtds+%3C+%5Cinfty+&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;int_{[a,b]^2}|k(s,t)|^2dtds &lt; &#92;infty ' title='&#92;int_{[a,b]^2}|k(s,t)|^2dtds &lt; &#92;infty ' class='latex' />.</p>
<p>Ist Null kein Eigenwert, so kann man kann dann die Operatoratornorm als <img src='http://s0.wp.com/latex.php?latex=1%2F%5Csqrt%7B%5CLambda+_1%7D&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='1/&#92;sqrt{&#92;Lambda _1}' title='1/&#92;sqrt{&#92;Lambda _1}' class='latex' /> bestimmen, wobei <img src='http://s0.wp.com/latex.php?latex=%5CLambda+_1&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;Lambda _1' title='&#92;Lambda _1' class='latex' /> die kleines charakteristische Zahl von A^*A ist. Wieso diese letzte Aussage richtig ist, weiß ich nicht genau, und wofür sie gut ist noch weniger. Ich vermute die Notation in charakteristischen Zahlen anstelle von Eigenwerten war in den 60er Jahren üblicher.</p>
<p>Auf <strong>Seite 396</strong> werden Gleichungen erster Ordnung y=Ux und Gleichungen zweiter Ordnung y = x + Ux eingeführt.</p>
<p>Auf Seite 93 wird schon in dieser Richtung y = Ux mit <img src='http://s0.wp.com/latex.php?latex=y%28s%29%3Dx%28s%29+-+%5Clambda+%5Cint+_a%5Eb+k%28s%2Ct%29x%28t%29dt&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='y(s)=x(s) - &#92;lambda &#92;int _a^b k(s,t)x(t)dt' title='y(s)=x(s) - &#92;lambda &#92;int _a^b k(s,t)x(t)dt' class='latex' /> definiert und dann die Operatornorm für <img src='http://s0.wp.com/latex.php?latex=L%5E2+%5Cto+L%5E2&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='L^2 &#92;to L^2' title='L^2 &#92;to L^2' class='latex' /> als <img src='http://s0.wp.com/latex.php?latex=%5Ctext%7Bsup%7D_k+%7C1-%5Clambda+%2F+%5Clambda+_k%7C&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;text{sup}_k |1-&#92;lambda / &#92;lambda _k|' title='&#92;text{sup}_k |1-&#92;lambda / &#92;lambda _k|' class='latex' /> angegeben, wobei hier k symmetrisch ist, so dass <img src='http://s0.wp.com/latex.php?latex=A%5E%2A%3DA&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='A^*=A' title='A^*=A' class='latex' />.</p>
<p>Auf <strong>Seite 58</strong> wird in der Gleichung nach (1) benutzt, dass <img src='http://s0.wp.com/latex.php?latex=%5Ctext%7Bmes%7D%28T%29+%3D+%5Cmu+%28T%29&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;text{mes}(T) = &#92;mu (T)' title='&#92;text{mes}(T) = &#92;mu (T)' class='latex' /> endlich ist.  Vorher auf der Seite wird die Bemerkung am Ende der Seite referenziert, dass hier oBdA T=[0,1] anstatt irgendeiner auch Menge auch mit möglicherweise unendlichem Maß gewählt werden kann. Für Inklusionen <img src='http://s0.wp.com/latex.php?latex=L%5Eq%28T%2C%5Cmathbb%7BR%7D%29+%5Cto+L%5Ep%28T%2C%5Cmathbb%7BR%7D%29&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='L^q(T,&#92;mathbb{R}) &#92;to L^p(T,&#92;mathbb{R})' title='L^q(T,&#92;mathbb{R}) &#92;to L^p(T,&#92;mathbb{R})' class='latex' /> ist es aber entscheidend, dass die Menge T endliches Maß hat. Was soll dann dieses Bemerkung, dass [0,1] oBdA gewählt werden könnte?</p>
<p>Auf <strong>Seite 288 </strong>wird definiert <img src='http://s0.wp.com/latex.php?latex=Ux+%28s%29+%3D+y%28s%29%3D%5Cint+_D+k%28s%2Ct%29x%28t%29+dt&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='Ux (s) = y(s)=&#92;int _D k(s,t)x(t) dt' title='Ux (s) = y(s)=&#92;int _D k(s,t)x(t) dt' class='latex' /> für <img src='http://s0.wp.com/latex.php?latex=s%5Cin+D%27%2C+t%5Cin+D&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='s&#92;in D&#039;, t&#92;in D' title='s&#92;in D&#039;, t&#92;in D' class='latex' /> mit <img src='http://s0.wp.com/latex.php?latex=%5Cmu+%28D%29+%3C+%5Cinfty+&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;mu (D) &lt; &#92;infty ' title='&#92;mu (D) &lt; &#92;infty ' class='latex' />, <img src='http://s0.wp.com/latex.php?latex=%5Cmu+%28D%27%29+%3C+%5Cinfty+&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;mu (D&#039;) &lt; &#92;infty ' title='&#92;mu (D&#039;) &lt; &#92;infty ' class='latex' />, <img src='http://s0.wp.com/latex.php?latex=%5Ctext%7Bess-sup%7D_s+%7C%7C+k%28s%2Ct%29+%7C%7C_%7Bt%2CL%5Er%7D+%5Cleq+C_1&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;text{ess-sup}_s || k(s,t) ||_{t,L^r} &#92;leq C_1' title='&#92;text{ess-sup}_s || k(s,t) ||_{t,L^r} &#92;leq C_1' class='latex' /> fast überall, <img src='http://s0.wp.com/latex.php?latex=%5Ctext%7Bess-sup%7D_s+%7C%7C+k%28s%2Ct%29+%7C%7C_%7Bs%2CL%5E%7B%5Csigma+%7D%7D+%5Cleq+C_2&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;text{ess-sup}_s || k(s,t) ||_{s,L^{&#92;sigma }} &#92;leq C_2' title='&#92;text{ess-sup}_s || k(s,t) ||_{s,L^{&#92;sigma }} &#92;leq C_2' class='latex' /> fast überall, <img src='http://s0.wp.com/latex.php?latex=q%5Cgeq+p&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='q&#92;geq p' title='q&#92;geq p' class='latex' />, <img src='http://s0.wp.com/latex.php?latex=q%5Cgeq+%5Csigma&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='q&#92;geq &#92;sigma' title='q&#92;geq &#92;sigma' class='latex' />, <img src='http://s0.wp.com/latex.php?latex=%281-%5Csigma+%2F+p%29p%27%5Cgeq+r&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='(1-&#92;sigma / p)p&#039;&#92;geq r' title='(1-&#92;sigma / p)p&#039;&#92;geq r' class='latex' /> [hier wie üblich <img src='http://s0.wp.com/latex.php?latex=p%5E%7B-1%7D%2Bp%27%5E%7B-1%7D%3D1&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='p^{-1}+p&#039;^{-1}=1' title='p^{-1}+p&#039;^{-1}=1' class='latex' />]. Unter all diesen Voraussetzungen ist <img src='http://s0.wp.com/latex.php?latex=U+%3A+L%5Ep%28D%2C%5Cmathbb%7BR%7D%29+%5Cto+L%5Eq%28D%27%2C+%5Cmathbb%7BR%7D%29&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='U : L^p(D,&#92;mathbb{R}) &#92;to L^q(D&#039;, &#92;mathbb{R})' title='U : L^p(D,&#92;mathbb{R}) &#92;to L^q(D&#039;, &#92;mathbb{R})' class='latex' /> und die Operatornorm ist kleiner als <img src='http://s0.wp.com/latex.php?latex=C_1%5E%7B1-%5Csigma+%2F+p%7DC_2%5E%7B%5Csigma+%2Fq%7D&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='C_1^{1-&#92;sigma / p}C_2^{&#92;sigma /q}' title='C_1^{1-&#92;sigma / p}C_2^{&#92;sigma /q}' class='latex' />. Dies wird in C.L. Smolitzki &#8220;Über die Summeirbarkeit von Potentialen&#8221;, Uspetchi. Matem. Nouk. 12 (1957) 4, 349-356 verallgemeinert.</p>
<p>Auf <strong>Seite 290</strong> die Aussage von Seite 288 kann man erweitern auf den Fall, dass die eine Konstante von s abhängt: <img src='http://s0.wp.com/latex.php?latex=%5Cint+_D+%7Ck%28s%2Ct%29%7C%5Er+dt%7C%5E%7B1%2Fr%7D+%5Cleq+C_1%5CPsi+%28s%29&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;int _D |k(s,t)|^r dt|^{1/r} &#92;leq C_1&#92;Psi (s)' title='&#92;int _D |k(s,t)|^r dt|^{1/r} &#92;leq C_1&#92;Psi (s)' class='latex' /> mit <img src='http://s0.wp.com/latex.php?latex=%5Cint+_%7BD%27%7D+%5Cleft%28+%7Ck%28s%2Ct%29%7C%28%5CPsi%28s%29%29%5E%7Bq%2F%5Csigma+-1%7D+%5Cright%29+%5E%7B%5Csigma+%7D+d+s+%5Cleq+C_2&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;int _{D&#039;} &#92;left( |k(s,t)|(&#92;Psi(s))^{q/&#92;sigma -1} &#92;right) ^{&#92;sigma } d s &#92;leq C_2' title='&#92;int _{D&#039;} &#92;left( |k(s,t)|(&#92;Psi(s))^{q/&#92;sigma -1} &#92;right) ^{&#92;sigma } d s &#92;leq C_2' class='latex' /> und <img src='http://s0.wp.com/latex.php?latex=%7C%7Ck%7C%7C_%7BL%5E%7Br%27%7D%28D+%5Ctimes+D%27%29%7D+%5Cleq+C.&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='||k||_{L^{r&#039;}(D &#92;times D&#039;)} &#92;leq C.' title='||k||_{L^{r&#039;}(D &#92;times D&#039;)} &#92;leq C.' class='latex' /> Dann gilt <img src='http://s0.wp.com/latex.php?latex=A_k&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='A_k' title='A_k' class='latex' /> (in meiner Nomenklatur der lineare Operator zum Kern k) ist linear und vollstetig (vollstetig = stetig + kompakt) als Operator <img src='http://s0.wp.com/latex.php?latex=L%5Ep+%5Cto+L%5Eq&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='L^p &#92;to L^q' title='L^p &#92;to L^q' class='latex' />. Hierbei ist <img src='http://s0.wp.com/latex.php?latex=r%3D+%5Ctext%7Bmin%7D%28p%2Cq%27%29&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='r= &#92;text{min}(p,q&#039;)' title='r= &#92;text{min}(p,q&#039;)' class='latex' /> und <img src='http://s0.wp.com/latex.php?latex=r%5E%7B-1%7D%2Br%27%5E%7B-1%7D%3D1&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='r^{-1}+r&#039;^{-1}=1' title='r^{-1}+r&#039;^{-1}=1' class='latex' />.</p>
<p>Auf <strong>Seite 293 </strong>gibt es dann noch die folgende Variante: <img src='http://s0.wp.com/latex.php?latex=%5Cint+_D+%5Cleft%5B+%7C%5Ctext%7Bgrad%7D_s+k+%28s%2Ct%29%7C+%7Cs-t%7C%5E%7B1-%5Cbeta%7D%5Cright%5D%5Er+d+t+%5E%7B1%2Fr%7D+%5Cleq+E&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;int _D &#92;left[ |&#92;text{grad}_s k (s,t)| |s-t|^{1-&#92;beta}&#92;right]^r d t ^{1/r} &#92;leq E' title='&#92;int _D &#92;left[ |&#92;text{grad}_s k (s,t)| |s-t|^{1-&#92;beta}&#92;right]^r d t ^{1/r} &#92;leq E' class='latex' /> und <img src='http://s0.wp.com/latex.php?latex=%5Cint+_D%5Cfrac%7B%7Ck%28s%2Ct%29%7C%7D%7B%7Cs-t%7C%5E%7B%5Cbeta+%7D%7Dd+t+%5Cleq+F&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;int _D&#92;frac{|k(s,t)|}{|s-t|^{&#92;beta }}d t &#92;leq F' title='&#92;int _D&#92;frac{|k(s,t)|}{|s-t|^{&#92;beta }}d t &#92;leq F' class='latex' />, dann ist <img src='http://s0.wp.com/latex.php?latex=A_k+%3A+L%5E%7Br%27%7D%28D%2C%5Cmathbb%7BR%7D%29+%5Cto+%5Ctext%7BLip%7D+%5Cbeta&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='A_k : L^{r&#039;}(D,&#92;mathbb{R}) &#92;to &#92;text{Lip} &#92;beta' title='A_k : L^{r&#039;}(D,&#92;mathbb{R}) &#92;to &#92;text{Lip} &#92;beta' class='latex' /> stetig. Hier steht <img src='http://s0.wp.com/latex.php?latex=%5Ctext%7BLip%7D+%5Cbeta&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;text{Lip} &#92;beta' title='&#92;text{Lip} &#92;beta' class='latex' /> für den Raum der <img src='http://s0.wp.com/latex.php?latex=%5Cbeta+&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;beta ' title='&#92;beta ' class='latex' />-Lipschitz-stetigen Funktionen, dieser Raum wird in meiner Nomenklatur bezeichnet als <img src='http://s0.wp.com/latex.php?latex=%7BC%7D%5E%7B0%2C+%5Cbeta+%7D%28M%2C%5Cmathbb%7BR%7D%29&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='{C}^{0, &#92;beta }(M,&#92;mathbb{R})' title='{C}^{0, &#92;beta }(M,&#92;mathbb{R})' class='latex' />. Man erhält darüber hinaus die Aussage, dass <img src='http://s0.wp.com/latex.php?latex=A_k+%3A+L%5E%7Br%27%7D%28D%2C%5Cmathbb%7BR%7D%29+%5Cto+C%5E0&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='A_k : L^{r&#039;}(D,&#92;mathbb{R}) &#92;to C^0' title='A_k : L^{r&#039;}(D,&#92;mathbb{R}) &#92;to C^0' class='latex' /> sogar vollstetig (stetig + kompakt) ist.</p>
<p>Auf <strong>Seite 296 </strong>wird dann eine spezielle Form des Kernes k betrachtet. Und zwar soll gelten <img src='http://s0.wp.com/latex.php?latex=k%28s%2Ct%29%3D+%5Cfrac%7BB%28s%2Ct%29%7D%7B%7Cs-t%7C%5Em%7D&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='k(s,t)= &#92;frac{B(s,t)}{|s-t|^m}' title='k(s,t)= &#92;frac{B(s,t)}{|s-t|^m}' class='latex' /> für <img src='http://s0.wp.com/latex.php?latex=s+%5Cin+D%27%2C+t%5Cin+D%2C+D%5Csubset+%5Cmathbb%7BR%7D%5E%5Cmu+%2C+D%27%5Csubset+%5Cmathbb%7BR%7D%5E%5Cnu&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='s &#92;in D&#039;, t&#92;in D, D&#92;subset &#92;mathbb{R}^&#92;mu , D&#039;&#92;subset &#92;mathbb{R}^&#92;nu' title='s &#92;in D&#039;, t&#92;in D, D&#92;subset &#92;mathbb{R}^&#92;mu , D&#039;&#92;subset &#92;mathbb{R}^&#92;nu' class='latex' />, wobei man dann <img src='http://s0.wp.com/latex.php?latex=%5Cmathbb%7BR%7D%5E%5Cnu%5Csubset+%5Cmathbb%7BR%7D%5E%5Cmu&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;mathbb{R}^&#92;nu&#92;subset &#92;mathbb{R}^&#92;mu' title='&#92;mathbb{R}^&#92;nu&#92;subset &#92;mathbb{R}^&#92;mu' class='latex' /> oder <img src='http://s0.wp.com/latex.php?latex=%5Cmathbb%7BR%7D%5E%5Cmu%5Csubset+%5Cmathbb%7BR%7D%5E%5Cnu&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;mathbb{R}^&#92;mu&#92;subset &#92;mathbb{R}^&#92;nu' title='&#92;mathbb{R}^&#92;mu&#92;subset &#92;mathbb{R}^&#92;nu' class='latex' /> annimmt, um in dem gemeinsamen Raum die Differenz bilden zu können. Hier wird außerdem angenommen, dass <img src='http://s0.wp.com/latex.php?latex=B%28s%2Ct%29&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='B(s,t)' title='B(s,t)' class='latex' /> beschränkt ist und stetig für <img src='http://s0.wp.com/latex.php?latex=s+%5Cnot%3D+t&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='s &#92;not= t' title='s &#92;not= t' class='latex' />. Desweiteren wird angenommen <img src='http://s0.wp.com/latex.php?latex=m%2B%5Cbeta+%3C+%5Cmu+&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='m+&#92;beta &lt; &#92;mu ' title='m+&#92;beta &lt; &#92;mu ' class='latex' /> ,<img src='http://s0.wp.com/latex.php?latex=%5Ctext%7Bsup%7D_%7Bs%5Cin+D%27%7D%5Cleft%28+%5Cint+_D+%5Cfrac%7B+%7B%7C+%5Ctext%7Bgrad%7D+_s+B%28s%2Ct%29+%7C%7D%5Er++%7D%7B%7Cs-t%7C%5E%7B%28m%2B%5Cbeta+-1%29r%7D%7D+d+t%5Cright%29+%5E%7B1%2Fr%7D%5Cleq+E&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;text{sup}_{s&#92;in D&#039;}&#92;left( &#92;int _D &#92;frac{ {| &#92;text{grad} _s B(s,t) |}^r  }{|s-t|^{(m+&#92;beta -1)r}} d t&#92;right) ^{1/r}&#92;leq E' title='&#92;text{sup}_{s&#92;in D&#039;}&#92;left( &#92;int _D &#92;frac{ {| &#92;text{grad} _s B(s,t) |}^r  }{|s-t|^{(m+&#92;beta -1)r}} d t&#92;right) ^{1/r}&#92;leq E' class='latex' />. Dann gilt <img src='http://s0.wp.com/latex.php?latex=A_k+%3A+L%5Ep+%28D%2C%5Cmathbb%7BR%7D%29+%5Cto+%7BC%7D%5E%7B0%2C%5Cbeta+%7D+%28D%27+%2C%5Cmathbb%7BR%7D%29&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='A_k : L^p (D,&#92;mathbb{R}) &#92;to {C}^{0,&#92;beta } (D&#039; ,&#92;mathbb{R})' title='A_k : L^p (D,&#92;mathbb{R}) &#92;to {C}^{0,&#92;beta } (D&#039; ,&#92;mathbb{R})' class='latex' />. (keine Garantie, dass ich hier alle Voraussetzungen mit abgeschrieben haben, meine Notizen sind da etwas unklar, und das Buch liegt gerade nicht neben mir.)</p>
<p>Auf <strong>Seite 298</strong> ergibt sich dann weiter für so ein k dieser speziellen Form, dass für <img src='http://s0.wp.com/latex.php?latex=%28%5Cmu+-m%29p+%3E+%5Cmu+&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='(&#92;mu -m)p &gt; &#92;mu ' title='(&#92;mu -m)p &gt; &#92;mu ' class='latex' /> der Operator <img src='http://s0.wp.com/latex.php?latex=A_k+%3A+L%5Ep+%28D%2C%5Cmathbb%7BR%7D%29+%5Cto+%7BC%7D%5E%7B0%7D+%28D%27+%2C%5Cmathbb%7BR%7D%29&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='A_k : L^p (D,&#92;mathbb{R}) &#92;to {C}^{0} (D&#039; ,&#92;mathbb{R})' title='A_k : L^p (D,&#92;mathbb{R}) &#92;to {C}^{0} (D&#039; ,&#92;mathbb{R})' class='latex' /> stetig und kompakt ist. (Apropos: Ich vermute man definiert normalerweise kompakt nur für stetige Operatoren, so dass erstes wahrscheinlich gar nicht erwähnt werden muss.)</p>
<p>Auf <strong>Seite 335 </strong>habe ich die Frage: Wie wählt er da <img src='http://s0.wp.com/latex.php?latex=V%5Ccap+-V&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='V&#92;cap -V' title='V&#92;cap -V' class='latex' /> und nicht einfach <img src='http://s0.wp.com/latex.php?latex=V&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='V' title='V' class='latex' /> als Menge? Weißt das jemand?</p>
<p>Auf<strong> Seite 432</strong> wird wieder ein Operator mit einem stetigen Kern <img src='http://s0.wp.com/latex.php?latex=k%3A+%5B0%2C1%5D%5E2%5Cto+%5Cmathbb%7BR%7D&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='k: [0,1]^2&#92;to &#92;mathbb{R}' title='k: [0,1]^2&#92;to &#92;mathbb{R}' class='latex' />  betrachtet. Wieder ist die Operatornorm von <img src='http://s0.wp.com/latex.php?latex=A_k%3AC%5E0+%5Cto+C%5E0&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='A_k:C^0 &#92;to C^0' title='A_k:C^0 &#92;to C^0' class='latex' /> gegeben durch <img src='http://s0.wp.com/latex.php?latex=%5Ctext%7Bmax%7D+_%7Bs+%5Cin+%5B0%2C1%5D+%7D+%5Cint+_0%5E1+%7C+k%28s%2Ct%29+%7C+d+t&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;text{max} _{s &#92;in [0,1] } &#92;int _0^1 | k(s,t) | d t' title='&#92;text{max} _{s &#92;in [0,1] } &#92;int _0^1 | k(s,t) | d t' class='latex' />. Es wird dann ein Operator definiert mittels <img src='http://s0.wp.com/latex.php?latex=y%3D%5Ctilde%7BU%7D%3Dx-%5Clambda+A_k+x&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='y=&#92;tilde{U}=x-&#92;lambda A_k x' title='y=&#92;tilde{U}=x-&#92;lambda A_k x' class='latex' />. Es wird gezeigt: Dieser ist lösbar für <img src='http://s0.wp.com/latex.php?latex=%5Clambda+%3C+%7C%7CA_k%7C%7C_%7BC%5E0%5Cto+C%5E0%7D&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;lambda &lt; ||A_k||_{C^0&#92;to C^0}' title='&#92;lambda &lt; ||A_k||_{C^0&#92;to C^0}' class='latex' /> (siehe dazu auch S. 149ff). Es werden dann iterierte Kerne betrachtet. Iterierte Kerne sind die Kerne für die Operatoren <img src='http://s0.wp.com/latex.php?latex=%28A_k%29%5Ei%3DB%5Ei&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='(A_k)^i=B^i' title='(A_k)^i=B^i' class='latex' /> für <img src='http://s0.wp.com/latex.php?latex=i%5Cin+%5Cmathbb%7BN%7D&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='i&#92;in &#92;mathbb{N}' title='i&#92;in &#92;mathbb{N}' class='latex' />. Man betrachtet dann <img src='http://s0.wp.com/latex.php?latex=B%3D%5Csum+_i+%5Clambda+%5E%7Bi-1%7DA_k%5Ei&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='B=&#92;sum _i &#92;lambda ^{i-1}A_k^i' title='B=&#92;sum _i &#92;lambda ^{i-1}A_k^i' class='latex' /> um dies als Lösungsoperator für <img src='http://s0.wp.com/latex.php?latex=%5Ctilde%7BU%7D&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;tilde{U}' title='&#92;tilde{U}' class='latex' /> zu erkennen. Es wird dann der Kern zum Operator B betrachtet und überlegt in welcher Weise die Kerne der Partialsummen gegen diesen Kern konvergieren. Die Kerne <img src='http://s0.wp.com/latex.php?latex=k_%7BB%5Ei%7D&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='k_{B^i}' title='k_{B^i}' class='latex' /> zu <img src='http://s0.wp.com/latex.php?latex=B%5Ei&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='B^i' title='B^i' class='latex' /> ergeben sich dann per Iteration mittels <img src='http://s0.wp.com/latex.php?latex=k_%7BB%5E%7Bi%2B1%7D%7D%28s%2Cu%29+%3D+%5Cint+_0%5E1+k_%7BB%5E%7Bi%2B1%7D%7D%28s%2Ct%29k%28t%2Cu%29+d+t&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='k_{B^{i+1}}(s,u) = &#92;int _0^1 k_{B^{i+1}}(s,t)k(t,u) d t' title='k_{B^{i+1}}(s,u) = &#92;int _0^1 k_{B^{i+1}}(s,t)k(t,u) d t' class='latex' />. Und für <img src='http://s0.wp.com/latex.php?latex=%5Clambda+&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;lambda ' title='&#92;lambda ' class='latex' /> klein genug erhält man die Konvergenz der Kerne für festes t &#8211; aber gleichmäßig in t &#8211; wenn man die Funktionen <img src='http://s0.wp.com/latex.php?latex=k_%7BB%5Ei%7D%28s%2Ct%29&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='k_{B^i}(s,t)' title='k_{B^i}(s,t)' class='latex' /> im Raum <img src='http://s0.wp.com/latex.php?latex=L%5E1&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='L^1' title='L^1' class='latex' /> bezüglich der Variable s betrachtet.  [Achtung: Hier weicht meine Notation von der von Kantarowitsch und Akilow ab.]</p>
<p>Auf <strong>Seite 440</strong> habe ich die Frage: Was sind denn die Voraussetzungen dafür das eine Projektion exisiert? Was braucht man zusätzlich zu den folgenden Voraussetzungen: X normierte Vektorraum, <img src='http://s0.wp.com/latex.php?latex=%5Ctilde%7BX%7D+%5Csubset+X&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;tilde{X} &#92;subset X' title='&#92;tilde{X} &#92;subset X' class='latex' /> ein Teilraum, <img src='http://s0.wp.com/latex.php?latex=%5Ctilde%7BX%7D&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;tilde{X}' title='&#92;tilde{X}' class='latex' /> vollständig, X nicht zwingend vollständig. Braucht man noch eine weitere Bedingungen dafür, dass eine Projektion <img src='http://s0.wp.com/latex.php?latex=P%3A+X+%5Cto+X&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='P: X &#92;to X' title='P: X &#92;to X' class='latex' /> auf <img src='http://s0.wp.com/latex.php?latex=tilde%7BX%7D&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='tilde{X}' title='tilde{X}' class='latex' /> existiert?</p>
<p>Auf <strong>Seite 441</strong> bin ich unsicher, was das da heißt. Was sind die Quantoren vor <img src='http://s0.wp.com/latex.php?latex=%5Cmu+_1+%2C+%5Cmu+_2&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;mu _1 , &#92;mu _2' title='&#92;mu _1 , &#92;mu _2' class='latex' />? Meinen sie <img src='http://s0.wp.com/latex.php?latex=%5Cexists+&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;exists ' title='&#92;exists ' class='latex' /> oder <img src='http://s0.wp.com/latex.php?latex=%5Cforall+&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;forall ' title='&#92;forall ' class='latex' />?  Ich denke <img src='http://s0.wp.com/latex.php?latex=%5Cforall+%5Cmu+_1+%2C+%5Cmu+_2&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;forall &#92;mu _1 , &#92;mu _2' title='&#92;forall &#92;mu _1 , &#92;mu _2' class='latex' /> macht mehr Sinn. Auf der anderen Seite hängt wohl <img src='http://s0.wp.com/latex.php?latex=%5Cmu+_2&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;mu _2' title='&#92;mu _2' class='latex' /> von y nicht ab. <img src='http://s0.wp.com/latex.php?latex=%5Cmu+_1&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;mu _1' title='&#92;mu _1' class='latex' /> und <img src='http://s0.wp.com/latex.php?latex=%5Cmu+&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;mu ' title='&#92;mu ' class='latex' /> hängen aber schon von y ab. Da kann es ja dann eigentlich nicht &#8220;für alle&#8221; sein. Hm. Hilft da jemand?</p>
<p>Auf <strong>Seite 490</strong> habe ich die Frage: Wie soll ich hier die Referenz auf IX.4.3 vertsehen? Wann hat man denn im Allgemeinen schon einen Operator dessen Spektrum beschränkt ist?  [jetzt habe ich das in meiner Anwendung, für die ich das Buch gelesen habe, nicht.]</p>
<p>Auf <strong>Seite 529</strong> ist k meßbar aber nicht unbedingt stetig!!! Aber es gibt andere Voraussetzungen. Hier wird die Gleichung <img src='http://s0.wp.com/latex.php?latex=x%28s%29%3D%5Clambda+%5Cint_a%5Eb+%5Cphi+%28s%2Ct%2Cx%28t%29%29+d+t&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='x(s)=&#92;lambda &#92;int_a^b &#92;phi (s,t,x(t)) d t' title='x(s)=&#92;lambda &#92;int_a^b &#92;phi (s,t,x(t)) d t' class='latex' /> betrachtet. Es wird nun gefordert, dass <img src='http://s0.wp.com/latex.php?latex=%5Cphi+&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;phi ' title='&#92;phi ' class='latex' /> die folgende Form hat: <img src='http://s0.wp.com/latex.php?latex=%5Cphi+%28s%2Ct%2Cu%29%3D+K%28s%2Ct%29%5Cpsi+%28t%2Cu%29&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;phi (s,t,u)= K(s,t)&#92;psi (t,u)' title='&#92;phi (s,t,u)= K(s,t)&#92;psi (t,u)' class='latex' />. Nun fordert man, dass <img src='http://s0.wp.com/latex.php?latex=%5Cpsi+&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;psi ' title='&#92;psi ' class='latex' /> auf <img src='http://s0.wp.com/latex.php?latex=%5Ba%2Cb%5D%5Ctimes+%5B-h%2Ch%5D&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='[a,b]&#92;times [-h,h]' title='[a,b]&#92;times [-h,h]' class='latex' /> definiert und stetig ist. Außerdem sei <img src='http://s0.wp.com/latex.php?latex=K&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='K' title='K' class='latex' /> auf <img src='http://s0.wp.com/latex.php?latex=%5Ba%2Cb%5D%5E2&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='[a,b]^2' title='[a,b]^2' class='latex' /> definiert und dort gelte <img src='http://s0.wp.com/latex.php?latex=A%5E2+%3D+%5Ctext%7Bsup%7D_%7Bs%5Cin+%5Ba%2Cb%5D%7D%5Cint+_a%5Eb+%7CK%28s%2Ct%29%7C%5E2+d+t+%3C+%5Cinfty+&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='A^2 = &#92;text{sup}_{s&#92;in [a,b]}&#92;int _a^b |K(s,t)|^2 d t &lt; &#92;infty ' title='A^2 = &#92;text{sup}_{s&#92;in [a,b]}&#92;int _a^b |K(s,t)|^2 d t &lt; &#92;infty ' class='latex' />. Die Gleichung hat dann eine auf  [a,b] quadratisch summierbare Lösung, wenn <img src='http://s0.wp.com/latex.php?latex=%7C%5Clambda+%7C+%5Cleq+%5Cfrac%7Bq%7D%7BAM_2%5Csqrt%7Bb-a%7D%7D&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='|&#92;lambda | &#92;leq &#92;frac{q}{AM_2&#92;sqrt{b-a}}' title='|&#92;lambda | &#92;leq &#92;frac{q}{AM_2&#92;sqrt{b-a}}' class='latex' /> wobei <img src='http://s0.wp.com/latex.php?latex=M_2%3D%5Ctext%7Bmax%7D_%7Ba%5Cleq+t+%5Cleq+b+%2C+%7Cu%7C%5Cleq+h%7D%7C%5Cpsi+%28t%2Cu%29%7C&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='M_2=&#92;text{max}_{a&#92;leq t &#92;leq b , |u|&#92;leq h}|&#92;psi (t,u)|' title='M_2=&#92;text{max}_{a&#92;leq t &#92;leq b , |u|&#92;leq h}|&#92;psi (t,u)|' class='latex' />. Man setzt dabei natürlich voraus, dass die Werte von x betragsmäßig nicht h übersteigen.</p>
<p>Auf <strong>Seite 544</strong> betrachtet man bilinear Operatoren <img src='http://s0.wp.com/latex.php?latex=B%28x%2Cx%27%29%3Dy&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='B(x,x&#039;)=y' title='B(x,x&#039;)=y' class='latex' />. Man kann machne diese Operatoren über die folgende Integralgleichung definieren: <img src='http://s0.wp.com/latex.php?latex=y%28s%29+%3D+%5Cint+_0%5E1%5Cint+_0%5E1+k%28s%2Ct%2Cu%29x%28t%29x%27%28u%29+d+t+du&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='y(s) = &#92;int _0^1&#92;int _0^1 k(s,t,u)x(t)x&#039;(u) d t du' title='y(s) = &#92;int _0^1&#92;int _0^1 k(s,t,u)x(t)x&#039;(u) d t du' class='latex' />. Dies kann man z.B. für k stetig betrachten und x und x&#8217; aus den Räumen <img src='http://s0.wp.com/latex.php?latex=C%5E0&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='C^0' title='C^0' class='latex' /> oder <img src='http://s0.wp.com/latex.php?latex=L%5Ep&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='L^p' title='L^p' class='latex' />. Im Folgenden werden dann aber nur Operatoren von der Form <img src='http://s0.wp.com/latex.php?latex=y%28s%29+%3D+%5Cint+_0%5E1k%28s%2Ct%2Ct%29x%28t%29x%27%28t%29+d+t&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='y(s) = &#92;int _0^1k(s,t,t)x(t)x&#039;(t) d t' title='y(s) = &#92;int _0^1k(s,t,t)x(t)x&#039;(t) d t' class='latex' /> betrachtet.</p>
<p>Die Norm für den Operator <img src='http://s0.wp.com/latex.php?latex=L%5Ep%28%5B0%2C1%5D%2C%5Cmathbb%7BR%7D%29%5Cto+L%5Ep%28%5B0%2C1%5D%2C%5Cmathbb%7BR%7D%29&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='L^p([0,1],&#92;mathbb{R})&#92;to L^p([0,1],&#92;mathbb{R})' title='L^p([0,1],&#92;mathbb{R})&#92;to L^p([0,1],&#92;mathbb{R})' class='latex' /> mit p&gt;2 ist: <img src='http://s0.wp.com/latex.php?latex=%5Cint+_0%5E1+%5Cleft%28+%5Cint+_0%5E1+%7B%7Ck%28s%2Ct%29%7C%7D%5E%7B%5Cfrac%7Bp%7D%7Bp-2%7D%7D+d+t+%5Cright%29%5E%7Bp-2%7D+d+s&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;int _0^1 &#92;left( &#92;int _0^1 {|k(s,t)|}^{&#92;frac{p}{p-2}} d t &#92;right)^{p-2} d s' title='&#92;int _0^1 &#92;left( &#92;int _0^1 {|k(s,t)|}^{&#92;frac{p}{p-2}} d t &#92;right)^{p-2} d s' class='latex' />.</p>
<p>Die Norm für den Operator <img src='http://s0.wp.com/latex.php?latex=L%5E2%28%5B0%2C1%5D%2C%5Cmathbb%7BR%7D%29%5Cto+L%5E2%28%5B0%2C1%5D%2C%5Cmathbb%7BR%7D%29&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='L^2([0,1],&#92;mathbb{R})&#92;to L^2([0,1],&#92;mathbb{R})' title='L^2([0,1],&#92;mathbb{R})&#92;to L^2([0,1],&#92;mathbb{R})' class='latex' /> ist: <img src='http://s0.wp.com/latex.php?latex=%5Cint+_0%5E1+%5Csup+_s+%7Ck%28s%2Ct%29%7C+d+t&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;int _0^1 &#92;sup _s |k(s,t)| d t' title='&#92;int _0^1 &#92;sup _s |k(s,t)| d t' class='latex' />.</p>
<p>Die Norm für den Operator <img src='http://s0.wp.com/latex.php?latex=C%5E0%28%5B0%2C1%5D%2C%5Cmathbb%7BR%7D%29%5Cto+C%5E0%28%5B0%2C1%5D%2C%5Cmathbb%7BR%7D%29&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='C^0([0,1],&#92;mathbb{R})&#92;to C^0([0,1],&#92;mathbb{R})' title='C^0([0,1],&#92;mathbb{R})&#92;to C^0([0,1],&#92;mathbb{R})' class='latex' /> ist: <img src='http://s0.wp.com/latex.php?latex=%5Cmax+_%7Bs%5Cin+%5B0%2C1%5D%7D+%5Cint+_0%5E1+%7Ck%28s%2Ct%29%7Cdt&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;max _{s&#92;in [0,1]} &#92;int _0^1 |k(s,t)|dt' title='&#92;max _{s&#92;in [0,1]} &#92;int _0^1 |k(s,t)|dt' class='latex' />.</p>
<p>Aus Seite <strong>548</strong> werden dann Gleichungen der Form <img src='http://s0.wp.com/latex.php?latex=y%3DP%28x%29&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='y=P(x)' title='y=P(x)' class='latex' /> mit <img src='http://s0.wp.com/latex.php?latex=y%28s%29%3D%5Cint+_0%5E1k%28s%2Ct%2Cx%28t%29%29+d+t&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='y(s)=&#92;int _0^1k(s,t,x(t)) d t' title='y(s)=&#92;int _0^1k(s,t,x(t)) d t' class='latex' /> betrachtet und geguckt, wann hier Differenzieren unter das Integral gezogen werden kann. Dafür wird vorausgesetzt, dass k stetig in allen Variablen gemeinsam und zweimal stetig differenzierbar in u ist, und weiter, dass <img src='http://s0.wp.com/latex.php?latex=%7C+%5Cfrac%7B%5Cpartial+%5E2%7D%7B%5Cpartial+u%5E2%7Dk%28s%2Ct%2Cu%29%7C%5Cleq+M%7B%7Cu%7C%7D%5E%7Bp-2%7D+%2B+N&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='| &#92;frac{&#92;partial ^2}{&#92;partial u^2}k(s,t,u)|&#92;leq M{|u|}^{p-2} + N' title='| &#92;frac{&#92;partial ^2}{&#92;partial u^2}k(s,t,u)|&#92;leq M{|u|}^{p-2} + N' class='latex' />. Dann ist <img src='http://s0.wp.com/latex.php?latex=P%3AL%5Ep%5Cto+L%5Eq&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='P:L^p&#92;to L^q' title='P:L^p&#92;to L^q' class='latex' /> ein stetiger Operator der zweimal differenzierbar ist in jedem <img src='http://s0.wp.com/latex.php?latex=x%5Cin+L%5Ep&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='x&#92;in L^p' title='x&#92;in L^p' class='latex' />. Die Ableitungen berechnen sich dann durch ziehen des Integrals unter das Integralzeichen: <img src='http://s0.wp.com/latex.php?latex=P%27%28x_0%29+x+%3D+%5Cint+_0%5E1+%5Cleft%28+%5Cfrac%7B%5Cpartial+%7D%7B%5Cpartial+u%7DK+%5Cright%29+%28s%2Ct%2Cx_o%28t%29%29+x%28t%29+d+t&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='P&#039;(x_0) x = &#92;int _0^1 &#92;left( &#92;frac{&#92;partial }{&#92;partial u}K &#92;right) (s,t,x_o(t)) x(t) d t' title='P&#039;(x_0) x = &#92;int _0^1 &#92;left( &#92;frac{&#92;partial }{&#92;partial u}K &#92;right) (s,t,x_o(t)) x(t) d t' class='latex' /> und <img src='http://s0.wp.com/latex.php?latex=P%27%27%28x_0%29+%28x%2Cx%27%29%3D+%5Cint+_0%5E1+%5Cleft%28+%5Cfrac%7B%5Cpartial+%5E2%7D%7B%5Cpartial+u+%5E2%7DK+%5Cright%29+%28s%2Ct%2Cx_o%28t%29%29+x%28t%29x%27%28t%29+d+t&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='P&#039;&#039;(x_0) (x,x&#039;)= &#92;int _0^1 &#92;left( &#92;frac{&#92;partial ^2}{&#92;partial u ^2}K &#92;right) (s,t,x_o(t)) x(t)x&#039;(t) d t' title='P&#039;&#039;(x_0) (x,x&#039;)= &#92;int _0^1 &#92;left( &#92;frac{&#92;partial ^2}{&#92;partial u ^2}K &#92;right) (s,t,x_o(t)) x(t)x&#039;(t) d t' class='latex' />. (p,q sind in diesen Zeilen unabhängig von einander. Es wird also in dieser Notation und auch sonst im Buch nicht q=p&#8217; mit <img src='http://s0.wp.com/latex.php?latex=p%27%5E%7B-1%7D%2Bp%5E%7B-1%7D%3D1&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='p&#039;^{-1}+p^{-1}=1' title='p&#039;^{-1}+p^{-1}=1' class='latex' /> gefordert.)</p>
<p>Auf <strong>Seite 549 </strong>denke ich, hat sich ein Schreibfehler eingeschlichen. Es sollte dort heißen: &#8220;Wir beweisen jetzt die Differenzierbarkeit des Operators <img src='http://s0.wp.com/latex.php?latex=P&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='P' title='P' class='latex' /> und die Beziehung <img src='http://s0.wp.com/latex.php?latex=P%27%28x_0%29%3DU&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='P&#039;(x_0)=U' title='P&#039;(x_0)=U' class='latex' />. Es sei <img src='http://s0.wp.com/latex.php?latex=z%3DU%28x%29&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='z=U(x)' title='z=U(x)' class='latex' />.&#8221; Hier endet das Zitat im Buch in meiner Auflage im Vergleich dazu auf <img src='http://s0.wp.com/latex.php?latex=z%3DU%28z%29&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='z=U(z)' title='z=U(z)' class='latex' />.</p>
<p>Auf <strong>Seite 588 </strong>wird dann ein Operator <img src='http://s0.wp.com/latex.php?latex=y%3DPx+%3D+x+-+%5Cint_0%5E1k%28s%2Ct%2Cx%28t%29%29+dt&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='y=Px = x - &#92;int_0^1k(s,t,x(t)) dt' title='y=Px = x - &#92;int_0^1k(s,t,x(t)) dt' class='latex' /> definiert für k stetig mit stetigen Ableitungen wo nötig. Gesucht wird dann ein x mit <img src='http://s0.wp.com/latex.php?latex=x%3DPx&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='x=Px' title='x=Px' class='latex' />.  Es wird dann vom Raum X gefordert, dass sich in diesem die Differenziation unter das Integralziehen lässt. (Anmerkung, z.B. glatte Funktionen auf kompakten Gebiet erfüllen dies ja, aber man kann bestimmt auch andere Bedingungen fordern.) Unter diesen Bedingungen gilt dann der Satz: Erfüllt k einige Bedingungen, so konverviert das Newton verfahren. Vergleiche hierzu den <a title="Satz von Kantorowitsch auf der deutschen Wikipedia" href="http://de.wikipedia.org/wiki/Satz_von_Kantorowitsch">wikipedia: Satz von Kantorowitsch</a>. (Dies hat aber nun schon nur noch sehr bedingt etwas mit dem Thema zu tun, weswegen ich das Buch gelesen habe.) Ab Seite 592 wird dann noch im Anschluss eine Weg gezeigt wie man unter bestimmten Voraussetzungen an die Gleichung <img src='http://s0.wp.com/latex.php?latex=y%3DPx&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='y=Px' title='y=Px' class='latex' />, diese Gleichung approximieren kann, um dann über die Lösungen dieser approximierten Gleichung an einen Startweg des Newtonverfahrens zu gelangen, der den Bedingungen des vorhergehenden Satzes genügt und so eine Konvergenz garantiert. (Ich hoffe, diese Zusammenfassung der letzten Seiten stimmt so, ich habe sie nur überfolgen, weil das nicht das war, was ich suchte.)</p>
<p>So, dass sollen meine Kommentare zu diesem Buch gewesen sein?</p>
<p>Hat irgendjemand anderes noch Kommentare? Oder noch besser: Hat jemand eine Zusammenstellung von Sätzen zu Integralkernen. Insbesondere über deren Existenz und deren Eigenschaften in Abhängigkeit Eigenschaften des zugehörigen Operators?</p>
<p>Und dann noch ein letzter Punkt: Wie bei meinem letzten Post zu einem Buch <a href="../2009/06/16/spin-geometry-by-h-blaine-lawson-jr-and-marie-louise-michelsohn-annotations-on-the-1989-version-of-isbn-0691085420/">Spin Geometry by H. Blaine Lawson Jr. and Marie-Louise Michelsohn – Annotations on the 1989 version of ISBN 0691085420</a> (siehe letzter Absatz:  &#8220;Is there a standard for annotating on-line errata for books?&#8221;) frage ich mich, wie ich diese Kommentare hätte so schreiben können, dass sie ein Computerprogramm ausliest.[Nicht vom Inhalt her nur von der exakten Position auf welche Stelle in welchem Buch sie sich bezieht.] Es wäre doch total praktisch, wenn jemand, der sich auf books.google.com oder auf einem ebook reader das Buch anguckt, am Rand angeboten bekommen würde welche Kommentar es just zu diesen Absatz des Buches im Internet gibt. Viele meiner Kommentare hier sind dafür nicht ganz so praktisch, weil sie ja nur zusammenfassen, was ein Leser des Buches schon gerade selbst gesehen hat. Aber z.B. die Kommentare zu Kommentare den Seiten 335, 440, 441, 490 und 549 würden sich an einem Buch gut machen. Und auch einen Kommentar an jedem <img src='http://s0.wp.com/latex.php?latex=%5Ctilde%7BM%7D&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='&#92;tilde{M}' title='&#92;tilde{M}' class='latex' />, dass das heute <img src='http://s0.wp.com/latex.php?latex=L%5E%5Cinfty+&amp;bg=ffffff&amp;fg=414141&amp;s=0' alt='L^&#92;infty ' title='L^&#92;infty ' class='latex' /> heißt, wäre praktisch. Und wenn die Notation in anderen Räumen der Welt anders ist als hier, dann sollte der Kommentar halt nur manchen Nutzern angezeigt werden, z.B. abhängig davon welche Bücher ich sonst so lese. Selbst wenn es sich um offene Fragen handelt, könnte der Leser der genau auf meinem Niveau das Buch liest Feedback bekommen, ob auch andere seine Fragen hat, jemand von niedrigerem Niveau könnte auf Problemstellungen aufmerksam gemacht werden und jemand vom höherem Niveau könnte mir gerade einen 2 Zeiler zu einer meiner Fragen schreiben und so für alle kommenden Leser die Frage klären. <a href="../2009/06/16/spin-geometry-by-h-blaine-lawson-jr-and-marie-louise-michelsohn-annotations-on-the-1989-version-of-isbn-0691085420/"><br />
</a></p>
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		<title>BBC Listen Again Service as downloadable RealAudio Stream</title>
		<link>http://gbideas.wordpress.com/2009/11/07/bbc-listen-again-service-as-downloadable-realaudio-stream/</link>
		<comments>http://gbideas.wordpress.com/2009/11/07/bbc-listen-again-service-as-downloadable-realaudio-stream/#comments</comments>
		<pubDate>Sat, 07 Nov 2009 19:10:01 +0000</pubDate>
		<dc:creator>gbideas</dc:creator>
				<category><![CDATA[radio]]></category>
		<category><![CDATA[streaming media]]></category>
		<category><![CDATA[Adobe Flash]]></category>
		<category><![CDATA[bbc]]></category>
		<category><![CDATA[Doctor Who]]></category>
		<category><![CDATA[download]]></category>
		<category><![CDATA[dumpstream]]></category>
		<category><![CDATA[iPlayer]]></category>
		<category><![CDATA[Listen Again]]></category>
		<category><![CDATA[mplayer]]></category>
		<category><![CDATA[PID]]></category>
		<category><![CDATA[ra]]></category>
		<category><![CDATA[Real Audio]]></category>
		<category><![CDATA[Real Player]]></category>
		<category><![CDATA[save]]></category>
		<category><![CDATA[Sisters of the Flame]]></category>
		<category><![CDATA[stream]]></category>
		<category><![CDATA[streaming]]></category>
		<category><![CDATA[webbIE]]></category>

		<guid isPermaLink="false">http://gbideas.wordpress.com/?p=102</guid>
		<description><![CDATA[How to get Real Player URLs for BBC Listen Again programmes. Go to iPlayer Real converter and turn the PID into a URL. This might not work forever as the BBC switched to Flash and wants to offer AAC and Windows Media. But for now the legacy Real Audio streams that can be downloaded and save with mplayer are still available.<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=gbideas.wordpress.com&amp;blog=7643295&amp;post=102&amp;subd=gbideas&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>How to get Real Player URLs for BBC Listen Again programmes? Go to the webpage <em>iPlayer Real converter</em> and turn the PID into a URL. This might not work forever as the BBC switched to Flash and wants to offer AAC and Windows Media streams instead of Real Audio. But for now the legacy Real Audio streams that can be downloaded and save with mplayer are still available.</p>
<p><span id="more-102"></span></p>
<h2>Short version:</h2>
<p><strong>Go to bbc.co.uk</strong> and <strong>choose</strong> the <strong>program </strong>you want to listen to.</p>
<p><strong>Find </strong>the <strong>iPlayer Progamme ID</strong>. (for example here was a link to &#8220;<em>More: programme information</em>&#8221; on some episode <a href="http://www.bbc.co.uk/programmes/b00rw1t1#synopsis">http://www.bbc.co.uk/programmes/<strong>b00rw1t1</strong>#synopsis</a> and the iPlayer Programme ID is <em>b00rw1t1</em>.</p>
<p>Go to <a href="http://www.iplayerconverter.co.uk/convert.aspx"><strong>http://www.iplayerconverter.co.uk/convert.aspx</strong></a> , paste the ID in the field and press convert.</p>
<p><strong>Copy </strong>the <strong>link </strong>under: <em><strong>RealAudio</strong> </em>-  <strong><em>URL to global RealAudio rm stream</em>:</strong></p>
<p>Download mplayer, start a console, <strong>move to the mplayer directory</strong> and <strong>execute</strong></p>
<p><strong>mplayer -dumpstream -dumpfile filename.ra [putcopiedURLhere]</strong></p>
<ul>
<li>This will create a RealAudio file <em>filename.ra</em> in the current directory.</li>
<li>If you replace &#8220;[putcopiedURLhere]&#8221; by the URL in the clipboard everything works fine. You don&#8217;t need any quotations marks and you have to replace the phrase [putcopiedURLhere] including the parenthesis. The console will, however, put out some error messages at the end as it will split the clipboard URL in four parts at the &#8220;&amp;&#8221;s. It will then try to execute the latter parts that look like: &#8220;BBC-UID&#8221; or &#8220;pid&#8221;. This will fail. If you, however, have some procresses by this name, it would be safer (though 4 sec more work) to cut the last part from the clipboard URL before putting it in the command line.</li>
<li>Be sure to choose a different filename for the next file, so you don&#8217;t overwrite the first one.</li>
</ul>
<h2>My longer blog post:</h2>
<p>Back in the days BBC used the RealPlayer for its Listen Again service. It supported inline use within the BBC website and streaming facilitating the standalone player. Then they created their BBC iPlayer which uses Adobe Flash. However, they still had a link to the .ram file which contains the link to the .ra RealAudio Stream.</p>
<p>But as you can read in the iPlayer help: <a title="Why am I no longer able to 'Listen Again' to BBC radio programmes on BBC iPlayer in RealMedia format?" href="http://iplayerhelp.external.bbc.co.uk/help/playing_programmes/local_radio_real_media">Why am I no longer able to &#8216;Listen Again&#8217; to BBC radio programmes on BBC iPlayer in RealMedia format?</a> The BBC turned of the RealPlayer suppoert on 22 October 2009 &#8211; &#8230; officially.</p>
<p>On the BBC Internet blog you can read the article: <a title="Improvements to BBC Local Radio online" href="http://www.bbc.co.uk/blogs/bbcinternet/2009/08/improvements_to_bbc_local_radi.html">Improvements to BBC Local Radio online</a>. The blog post is from August 2009. It states that Real Streams for Local Radio have been turned off. They plan to offer AAC and Windows Media streams. But this hasn&#8217;t been implemented yet. So one can only listen to Local Radio on the Flash-based iPlayer. (Links and information via <a href="http://www.iplayerconverter.co.uk/about.aspx">this site</a>)</p>
<p>But this is not true for National Radio like BBC Radio 4 or BBC7.</p>
<p>The old RealStreams still exist. At least for now. (And maybe only for Non-UK-users) Old links (looking like this rtsp://rmv8.bbc.net.uk/radio7/sat1700.ra? ) don&#8217;t work anymore.</p>
<p>The website offering WebbIE, the free web browser for blind people with little or no sight, complains about this step as the flash-player isn&#8217;t that accessivle. Read about it here: <a title="WebbIE: Accessible BBC iPlayer (Listen Again)" href="http://www.webbie.org.uk/accessiblebbc/">WebbIE: Accessible BBC iPlayer (Listen Again)</a></p>
<p>But it turns out there still is a way to get the Listen Again Real Audio Streams for Real Player. I read a <a title="Sprayfly  Record BBC Listen Again programs to MP3 in Ubuntu" href="http://sprayfly.com/2009/02/21/record-bbc-listen-again-programs-to-mp3-in-ubuntu/">blog post about a ubuntu script that&#8217;ll download the BBC Listen Again Stream, save it as wav via mplayer and convert it to a mp3 via LAME.</a> This directed my to the website <a title="iPlayer Real Converter" href="http://www.iplayerconverter.co.uk/">iPlayer Real Converter</a>. If you give the website a iPlayer PID or search through the schedule, it&#8217;ll give you a link to the RealPlayer Stream.</p>
<p>I, for example was interested in the current episode of Doctor Who that was broadcasted on BBC7. I will post some links here, but I guess they won&#8217;t work by the time you read this, as the 7 days will be over.</p>
<p>From either the <a href="http://www.bbc.co.uk/programmes/b009szrh">Overview page for Episode ( http://www.bbc.co.uk/programmes/b009szrh )</a> or the <a href="http://www.bbc.co.uk/programmes/b00nlyg5">Details page for the Episode ( http://www.bbc.co.uk/programmes/b00nlyg5 )</a> you can get to the iPlayer (http://www.bbc.co.uk/iplayer/console/b00nlyg5) , which will use Flash to play the episode.  Within the html of the iPlayer I couldn&#8217;t find a link the stream. Maybe I overlooked it. Maybe the Flash player is used to create a URL for the stream from the PID. The source code contains somethink like this:</p>
<pre>iplayer.semp.setMetaFiles({
flash: {
playlist: "http://www.bbc.co.uk/iplayer/playlist/b00nlyg5",
mp3: true,
aac: true,
aacLow: false
},
real: "",
wmp: ""</pre>
<p>http://www.bbc.co.uk/iplayer/playlist/b00nlyg5 is a XML file. It contains a lot of information like the image to be used. Or what shows might be similar. But I couldn&#8217;t find the stream &#8211; URL.</p>
<p>But iPlayer Real Converter will help you. If you go the Schedule of BBC which is retrieved from the BBC via an XML file the old lady is offering, you get a link to http://www.iplayerconverter.co.uk/pid/b00nlyg5/stream.aspx</p>
<p>You can easily exchange the PID b00nlyg5 to whatever PID you have in your case.</p>
<p>The link I got redirected me to a file on the BCC server called: RadioBridge_intl_2300_bbc_7.ram</p>
<p>It contained the following link to a Real Stream &#8220;rtsp://rmv8.bbc.net.uk:554/bbc7coyopa/bbc7_-_saturday_2300.ra?timestamp=1257135938&amp;pid=b00nly7h&amp;BBC-UID=3ac234671728faa09320b837d0fb0c3d184337f196774&amp;SSO2-UID=&#8221; [I changed the link slightly to obfuscate the UID - you can't use it anyhow because the seven days are over. (and I change the timestamp)]. But from my former experience with the BBC URLs you should be fine using &#8220;rtsp://rmv8.bbc.net.uk:554/bbc7coyopa/bbc7_-_saturday_2300.ra?&#8221;</p>
<p>You can play this link using Real Player of mPlayer. Maybe you can even use vlc.</p>
<p>Just a quick note:</p>
<p>In case you want to listen the stream on day number 8. You might be tempted to run</p>
<pre>mplayer -dumpstream -dumpfile FileNameEpisodeOfDoctorWho.Ra rtsp://rmv8.bbc.net.uk:554/bbc7coyopa/bbc7_-_saturday_2300.ra?</pre>
<p>which will put the file FileNameEpisodeOfDoctorWho.Ra into the current working directory. [If you want to use the full URL including the "&amp;"s, you should be aware that Windows will think the command ends at the '&amp;' and a new one starts at the '&amp;'. You'll have to but '"'s around the URL in that case.] You can open this file using RealPlayer or mplayer. You can also use the more advanced command line shown on the <a title="Sprayfly  Record BBC Listen Again programs to MP3 in Ubuntu" href="http://sprayfly.com/2009/02/21/record-bbc-listen-again-programs-to-mp3-in-ubuntu/">blog post about a ubuntu script that&#8217;ll download the BBC Listen Again Stream, save it as wav via mplayer and convert it to a mp3 via LAME.</a></p>
<p>I will let you choose the bitrate for LAME and choose a good cache size and bandwidth. And you&#8217;ll get a .wav file from mplayer. The .ra file I created with my mplayer command line isn&#8217;t a wav file but a Real Audio file.  The size is about 20MB per hour.</p>
<p>Disclaimer: I surely don&#8217;t recommend you to save the stream. They&#8217;ll play a repeat someday. You don&#8217;t need to circumvent their 7 day constraint.</p>
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<enclosure url="http://www.iplayerconverter.co.uk/pid/b00nlyg5/stream.aspx" length="0" type="audio/x-pn-realaudio" />
	
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		<title>Battery BL-4C bulging out in Nokia 6260</title>
		<link>http://gbideas.wordpress.com/2009/11/07/battery-bl-4c-bulging-out-in-nokia-6260/</link>
		<comments>http://gbideas.wordpress.com/2009/11/07/battery-bl-4c-bulging-out-in-nokia-6260/#comments</comments>
		<pubDate>Sat, 07 Nov 2009 18:05:44 +0000</pubDate>
		<dc:creator>gbideas</dc:creator>
				<category><![CDATA[hardware]]></category>
		<category><![CDATA[mobile phone]]></category>
		<category><![CDATA[6260]]></category>
		<category><![CDATA[accumulator]]></category>
		<category><![CDATA[akku]]></category>
		<category><![CDATA[battery]]></category>
		<category><![CDATA[bulge out]]></category>
		<category><![CDATA[bulging out]]></category>
		<category><![CDATA[error]]></category>
		<category><![CDATA[increase size]]></category>
		<category><![CDATA[nokia]]></category>
		<category><![CDATA[nokia 6260]]></category>
		<category><![CDATA[phone]]></category>
		<category><![CDATA[problem]]></category>

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		<description><![CDATA[My Nokia 6260 battery BL-4C is bulging out. Should I be worried? Others experience the same.<img alt="" border="0" src="http://stats.wordpress.com/b.gif?host=gbideas.wordpress.com&amp;blog=7643295&amp;post=99&amp;subd=gbideas&amp;ref=&amp;feed=1" width="1" height="1" />]]></description>
			<content:encoded><![CDATA[<p>My Nokia 6260 battery BL-4C is bulging out. Should I be worried? Might it explode? Others experience the same. I have links to their complains.<span id="more-99"></span></p>
<p><img title="More..." src="http://gbideas.wordpress.com/wp-includes/js/tinymce/plugins/wordpress/img/trans.gif" alt="" /></p>
<p>My Blog Post:</p>
<p>I use a Nokia 6260, which was probably bought in 2004 or 2005 or so.</p>
<p>Recently I&#8217;ve constantly been getting the message &#8220;Bei Entn. d. Sp.-karte werden al-le offenen Progr. geschlossen. Trotz-dem entnehmen?&#8221; (&#8220;Bei Entnahme der Speicherkarte werden alle offenen Programme geschlossen. Trotzdem entnehmen?&#8221; / removing your memory card will close all running programs. remove anyway?). I wasn&#8217;t sure what to make of them.</p>
<p>No I realize that the problem is that my battery a BL-4C is bulging out. It got so large that the sticker on it is peeling away. And the battery compartment is barely closing, leaving a 1,5mm slit on both sides.</p>
<p>It&#8217;s the original battery.</p>
<p>I hope it won&#8217;t explode on my or release some acid in my trouser pocket.</p>
<p>I&#8217;m not alone.  Someone <a href="http://www.fixya.com/support/t3219200-nokia_bl_4c_battery_bulging_out">posted the question over here</a>. But he didn&#8217;t get no answer.</p>
<p><a title="BL 4C battery has now expanded and bulged out!!! " href="http://discussions.europe.nokia.com/discussions/board/message?board.id=phones&amp;thread.id=22578">Nokia Support Discussions: BL 4C battery has now expanded and bulged out!!!</a> has a more interesting thread on the topic. Someone over there has precisely my problem and got as answers, that this is just the way old batteries behave, so he should expect to be compensated. And he is told that this might be very dangerous, so he should exchange the battery as soon as possible.</p>
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