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<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">Fourier Analysis on GL(n,R)</title>
<author><name sortKey="Gelbart, Stephen S" sort="Gelbart, Stephen S" uniqKey="Gelbart S" first="Stephen S." last="Gelbart">Stephen S. Gelbart</name>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">PMC</idno>
<idno type="pmid">16591814</idno>
<idno type="pmc">286183</idno>
<idno type="url">http://www.ncbi.nlm.nih.gov/pmc/articles/PMC286183</idno>
<idno type="RBID">PMC:286183</idno>
<date when="1970">1970</date>
<idno type="wicri:Area/Pmc/Corpus">000039</idno>
<idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Corpus" wicri:corpus="PMC">000039</idno>
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<sourceDesc><biblStruct><analytic><title xml:lang="en" level="a" type="main">Fourier Analysis on GL(n,R)</title>
<author><name sortKey="Gelbart, Stephen S" sort="Gelbart, Stephen S" uniqKey="Gelbart S" first="Stephen S." last="Gelbart">Stephen S. Gelbart</name>
</author>
</analytic>
<series><title level="j">Proceedings of the National Academy of Sciences of the United States of America</title>
<idno type="ISSN">0027-8424</idno>
<idno type="eISSN">1091-6490</idno>
<imprint><date when="1970">1970</date>
</imprint>
</series>
</biblStruct>
</sourceDesc>
</fileDesc>
<profileDesc><textClass></textClass>
</profileDesc>
</teiHeader>
<front><div type="abstract" xml:lang="en"><p>Two problems of Fourier analysis on <italic>GL</italic>
(<italic>n</italic>
,<bold>R</bold>
) are studied. The first concerns the decomposition of the additive Fourier operator in terms of the group representation theory of <italic>G</italic>
. The second concerns the analytic continuation of certain zeta-functions defined on <italic>G</italic>
. It is found that the generalized Gamma functions of Gelfand and Graev arise naturally in the solution of both these problems.</p>
</div>
</front>
</TEI>
<pmc article-type="research-article"><pmc-comment>The publisher of this article does not allow downloading of the full text in XML form.</pmc-comment>
<front><journal-meta><journal-id journal-id-type="nlm-ta">Proc Natl Acad Sci U S A</journal-id>
<journal-title>Proceedings of the National Academy of Sciences of the United States of America</journal-title>
<issn pub-type="ppub">0027-8424</issn>
<issn pub-type="epub">1091-6490</issn>
</journal-meta>
<article-meta><article-id pub-id-type="pmid">16591814</article-id>
<article-id pub-id-type="pmc">286183</article-id>
<article-categories><subj-group subj-group-type="heading"><subject>Physical Sciences: Mathematics</subject>
</subj-group>
</article-categories>
<title-group><article-title>Fourier Analysis on GL(n,R)</article-title>
</title-group>
<contrib-group><contrib contrib-type="author"><name><surname>Gelbart</surname>
<given-names>Stephen S.</given-names>
</name>
</contrib>
</contrib-group>
<aff id="af1">PRINCETON UNIVERSITY</aff>
<pub-date pub-type="ppub"><month>01</month>
<year>1970</year>
</pub-date>
<volume>65</volume>
<issue>1</issue>
<fpage>14</fpage>
<lpage>18</lpage>
<abstract><p>Two problems of Fourier analysis on <italic>GL</italic>
(<italic>n</italic>
,<bold>R</bold>
) are studied. The first concerns the decomposition of the additive Fourier operator in terms of the group representation theory of <italic>G</italic>
. The second concerns the analytic continuation of certain zeta-functions defined on <italic>G</italic>
. It is found that the generalized Gamma functions of Gelfand and Graev arise naturally in the solution of both these problems.</p>
</abstract>
</article-meta>
</front>
</pmc>
</record>
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