Multivariate Jacobi Polynomials and the Selberg Integral. II
- Authors: Olshansk G.1, Osinenko A.2
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Affiliations:
- Institute for Information Transmission Problems
- Department of Mathematics, Columbia University
- Issue: Vol 215, No 6 (2016)
- Pages: 755-768
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/237728
- DOI: https://doi.org/10.1007/s10958-016-2881-3
- ID: 237728
Cite item
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 a 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. Bibliography: 20 titles.
About the authors
G. Olshansk
Institute for Information Transmission Problems
Author for correspondence.
Email: olsh2007@gmail.com
Russian Federation, Moscow
A. Osinenko
Department of Mathematics, Columbia University
Email: olsh2007@gmail.com
United States, New York