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<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">THE PLANCHEREL FORMULA FOR SL(2) OVER A LOCAL FIELD<xref ref-type="fn" rid="fn1"><sup>*</sup></xref></title><author><name sortKey="Sally, P J" sort="Sally, P J" uniqKey="Sally P" first="P. J." last="Sally">P. J. Sally</name></author><author><name sortKey="Shalika, J A" sort="Shalika, J A" uniqKey="Shalika J" first="J. A." last="Shalika">J. A. Shalika</name></author></titleStmt><publicationStmt><idno type="wicri:source">PMC</idno><idno type="pmid">16591775</idno><idno type="pmc">223502</idno><idno type="url">http://www.ncbi.nlm.nih.gov/pmc/articles/PMC223502</idno><idno type="RBID">PMC:223502</idno><date when="1969">1969</date><idno type="wicri:Area/Pmc/Corpus">000038</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Corpus" wicri:corpus="PMC">000038</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a" type="main">THE PLANCHEREL FORMULA FOR SL(2) OVER A LOCAL FIELD<xref ref-type="fn" rid="fn1"><sup>*</sup></xref></title><author><name sortKey="Sally, P J" sort="Sally, P J" uniqKey="Sally P" first="P. J." last="Sally">P. J. Sally</name></author><author><name sortKey="Shalika, J A" sort="Shalika, J A" uniqKey="Shalika J" first="J. A." last="Shalika">J. A. Shalika</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="1969">1969</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en"><p>More than two decades ago, in his classical paper on the irreducible unitary representations of the Lorentz group, V. Bargmann initiated the concrete study of Fourier analysis on real Lie groups and obtained the analogue of the classical Fourier expansion theorem in the case of the Lorentz group. Since then the general theory for real semisimple Lie groups has been extensively developed, chiefly through the work of Harish-Chandra. More generally, one may consider groups defined by algebraic equations over locally compact fields, in particular local fields, and ask for an explicit Fourier expansion formula. In the present article the authors obtain this formula for the group <italic>SL</italic>(2).</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">16591775</article-id><article-id pub-id-type="pmc">223502</article-id><article-categories><subj-group subj-group-type="heading"><subject>Physical Sciences: Mathematics</subject></subj-group></article-categories><title-group><article-title>THE PLANCHEREL FORMULA FOR SL(2) OVER A LOCAL FIELD<xref ref-type="fn" rid="fn1"><sup>*</sup></xref></article-title></title-group><contrib-group><contrib contrib-type="author"><name><surname>Sally</surname><given-names>P. J.</given-names><suffix>Jr.</suffix></name></contrib><contrib contrib-type="author"><name><surname>Shalika</surname><given-names>J. A.</given-names></name></contrib></contrib-group><aff id="af1"><label></label>UNIVERSITY OF CHICAGO</aff><aff id="af2"><label></label>PRINCETON UNIVERSITY</aff><author-notes><fn id="fn1"><label>*</label><p> Research of the first author supported in part by NSF grant GP8855; research of the second author supported by a Sloan fellowship.</p></fn></author-notes><pub-date pub-type="ppub"><month>07</month><year>1969</year></pub-date><volume>63</volume><issue>3</issue><fpage>661</fpage><lpage>667</lpage><abstract><p>More than two decades ago, in his classical paper on the irreducible unitary representations of the Lorentz group, V. Bargmann initiated the concrete study of Fourier analysis on real Lie groups and obtained the analogue of the classical Fourier expansion theorem in the case of the Lorentz group. Since then the general theory for real semisimple Lie groups has been extensively developed, chiefly through the work of Harish-Chandra. More generally, one may consider groups defined by algebraic equations over locally compact fields, in particular local fields, and ask for an explicit Fourier expansion formula. In the present article the authors obtain this formula for the group <italic>SL</italic>(2).</p></abstract></article-meta></front></pmc></record>Pour manipuler ce document sous Unix (Dilib)
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