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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

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

This article is cited 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

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.

UDC: 517.987

Received: 19.08.2015

Language: English


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

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