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Zapiski Nauchnykh Seminarov POMI, 2015, Volume 436, Pages 199–218 (Mi znsl6168)  
This article is cited in 2 scientific papers (total in 2 papers)

Multivariate Jacobi polynomials and the Selberg integral. II

G. Olshanskia, A. Osinenkob

a Institute for Information Transmission Problems, Moscow, Russia
b Department of Mathematics, Columbia University, New York, USA
Full-text PDF (253 kB) Citations (2)
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Abstract: The problem of harmonic analysis for infinite-dimensional classical groups and symmetric spaces leads to a family of probability measures with infinite-dimensional support. In the present paper, we construct these measures in a different way, which makes it possible to substantially extend the range of the parameters. The measures that we obtain can be interpreted as the result of formal analytic continuation of the $N$-dimensional beta distributions which appear in the Selberg integral. Our procedure of analytic continuation, based on Carlson's theorem, turns $N$ into a complex parameter.
Key words and phrases: Jacobi polynomials, Selberg integral, coherent families of measures.
Funding agency Grant number
Russian Science Foundation 14-50-00150
The research of G. Olshanski was carried out at the Institute for Information Transmission Problems of the Russian Academy of Sciences at the expense of the Russian Foundation for Sciences (project 14-50-00150).
Received: 19.08.2015
English version:
Journal of Mathematical Sciences (New York), 2016, Volume 215, Issue 6, Pages 755–768
DOI: https://doi.org/10.1007/s10958-016-2881-3
Bibliographic databases:
Document Type: Article
UDC: 517.987
Language: English
Citation: G. Olshanski, A. Osinenko, “Multivariate Jacobi polynomials and the Selberg integral. II”, Representation theory, dynamical systems, combinatorial methods. Part XXV, Zap. Nauchn. Sem. POMI, 436, POMI, St. Petersburg, 2015, 199–218; J. Math. Sci. (N. Y.), 215:6 (2016), 755–768
Citation in format AMSBIB
\Bibitem{OlsOsi15}
\by G.~Olshanski, A.~Osinenko
\paper Multivariate Jacobi polynomials and the Selberg integral.~II
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XXV
\serial Zap. Nauchn. Sem. POMI
\yr 2015
\vol 436
\pages 199--218
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6168}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3498194}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2016
\vol 215
\issue 6
\pages 755--768
\crossref{https://doi.org/10.1007/s10958-016-2881-3}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84966600923}
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  • https://www.mathnet.ru/eng/znsl/v436/p199
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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