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Zap. Nauchn. Sem. POMI, 2015, Volume 436, Pages 199–218 (Mi znsl6168)  

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

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).


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English version:
Journal of Mathematical Sciences (New York), 2016, 215:6, 755–768

Bibliographic databases:

UDC: 517.987
Received: 19.08.2015
Language:

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://www.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{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84966600923}


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