http://wiki.karljones.com/index.php?action=history&feed=atom&title=Resolvent_formalism 2026-10-23T17:15:08Z Revision history for this page on the wiki MediaWiki 1.24.2 http://wiki.karljones.com/index.php?title=Resolvent_formalism&diff=17195&oldid=prev 2016-08-25T02:11:36Z

<p></p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 02:11, 25 August 2016</td> </tr><tr><td colspan="2" class="diff-lineno">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>In [[mathematics]], the '''resolvent formalism''' is a technique for applying concepts from [[complex analysis]] to the study of the spectrum of operators on Banach spaces and more general spaces.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>In [[mathematics]], the '''resolvent formalism''' is a technique for applying concepts from [[complex analysis]] to the study of the spectrum of operators on <ins class="diffchange diffchange-inline">[[Banach space|</ins>Banach spaces<ins class="diffchange diffchange-inline">]] </ins>and more general spaces.</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The resolvent captures the spectral properties of an operator in the analytic structure of the resolvent. &#160;</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The resolvent captures the spectral properties of an operator in the analytic structure of the resolvent. &#160;</div></td></tr> <tr><td colspan="2" class="diff-lineno">Line 5:</td> <td colspan="2" class="diff-lineno">Line 5:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== See also ==</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== See also ==</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">* [[Banach space]]</ins></div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>* [[Compact operator]]</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>* [[Compact operator]]</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>* [[Decomposition of spectrum (functional analysis)]]</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>* [[Decomposition of spectrum (functional analysis)]]</div></td></tr> </table>

Karl Jones http://wiki.karljones.com/index.php?title=Resolvent_formalism&diff=17194&oldid=prev 2016-08-25T02:10:44Z

<p>Created page with &quot;In <a href="/index.php/Mathematics" title="Mathematics">mathematics</a>, the &#039;&#039;&#039;resolvent formalism&#039;&#039;&#039; is a technique for applying concepts from <a href="/index.php/Complex_analysis" title="Complex analysis">complex analysis</a> to the study of the spectrum of operators on Banach spaces and...&quot;</p> <p><b>New page</b></p><div>In [[mathematics]], the '''resolvent formalism''' is a technique for applying concepts from [[complex analysis]] to the study of the spectrum of operators on Banach spaces and more general spaces.<br /> <br /> The resolvent captures the spectral properties of an operator in the analytic structure of the resolvent. <br /> <br /> == See also ==<br /> <br /> * [[Compact operator]]<br /> * [[Decomposition of spectrum (functional analysis)]]<br /> * [[Fredholm theory]]<br /> * [[Holomorphic functional calculus]]<br /> * [[Laplace transform]]<br /> * [[Liouville-Neumann series]]<br /> * [[Resolvent set]]<br /> * [[Spectral theory]]<br /> * [[Stone's theorem on one-parameter unitary groups]]<br /> * [[Unbounded operator]]<br /> <br /> == External links ==<br /> <br /> * [https://en.wikipedia.org/wiki/Resolvent_formalism Resolvent formalism] @ Wikipedia<br /> <br /> <br /> [[Category:Mathematics]]</div>

Karl Jones