Generalized Tenney dual norms and Tp tuning space: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 511015690 - Original comment: ** |
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: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-05- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-05-24 16:56:55 UTC</tt>.<br> | ||
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The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html"> | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html"> | ||
[[image:mathhazard.jpg align=" | [[image:mathhazard.jpg align="left"]] | ||
=Dual Norms= | =Dual Norms= | ||
Given any [[Generalized Tenney Norms and Tp Interval Space|Tp norm]] on an interval space **Tp<span style="font-size: 10px; vertical-align: super;">G</span>** associated with a group **G**, we can define a corresponding **dual Tq* norm** on the dual space **Tq<span style="font-size: 10px; vertical-align: super;">G</span>*** which satisfies the following identity: | Given any [[Generalized Tenney Norms and Tp Interval Space|Tp norm]] on an interval space **Tp<span style="font-size: 10px; vertical-align: super;">G</span>** associated with a group **G**, we can define a corresponding **dual Tq* norm** on the dual space **Tq<span style="font-size: 10px; vertical-align: super;">G</span>*** which satisfies the following identity: | ||
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<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Generalized Tenney Dual Norms and Tp Tuning Space</title></head><body><br /> | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Generalized Tenney Dual Norms and Tp Tuning Space</title></head><body><br /> | ||
<!-- ws:start:WikiTextLocalImageRule:11: | <!-- ws:start:WikiTextLocalImageRule:11:&lt;img src=&quot;/file/view/mathhazard.jpg&quot; alt=&quot;&quot; title=&quot;&quot; align=&quot;left&quot; /&gt; --><img src="/file/view/mathhazard.jpg" alt="mathhazard.jpg" title="mathhazard.jpg" align="left" /><!-- ws:end:WikiTextLocalImageRule:11 --><br /> | ||
<!-- ws:start:WikiTextHeadingRule:5:&lt;h1&gt; --><h1 id="toc0"><a name="Dual Norms"></a><!-- ws:end:WikiTextHeadingRule:5 -->Dual Norms</h1> | |||
Given any <a class="wiki_link" href="/Generalized%20Tenney%20Norms%20and%20Tp%20Interval%20Space">Tp norm</a> on an interval space <strong>Tp<span style="font-size: 10px; vertical-align: super;">G</span></strong> associated with a group <strong>G</strong>, we can define a corresponding <strong>dual Tq* norm</strong> on the dual space <strong>Tq<span style="font-size: 10px; vertical-align: super;">G</span></strong>* which satisfies the following identity:<br /> | Given any <a class="wiki_link" href="/Generalized%20Tenney%20Norms%20and%20Tp%20Interval%20Space">Tp norm</a> on an interval space <strong>Tp<span style="font-size: 10px; vertical-align: super;">G</span></strong> associated with a group <strong>G</strong>, we can define a corresponding <strong>dual Tq* norm</strong> on the dual space <strong>Tq<span style="font-size: 10px; vertical-align: super;">G</span></strong>* which satisfies the following identity:<br /> | ||
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