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This article is cited in 6 scientific papers (total in 7 papers)
An analogue of the big $q$-Jacobi polynomials in the algebra of symmetric functions
G. I. Olshanskiiab a Institute for Information Transmission Problems of the Russian Academy of Sciences, Moscow, Russia
b Skolkovo Institute of Science and Technology (Skoltech), Moscow, Russia
Abstract:
It is well known how to construct a system of symmetric orthogonal polynomials in an arbitrary finite number of variables from an arbitrary system of orthogonal polynomials on the real line. In the special case of the big $q$-Jacobi polynomials, the number of variables can be made infinite. As a result, in the algebra of symmetric functions, there arises an inhomogeneous basis whose elements are orthogonal with respect to some probability measure. This measure is defined on a certain space of infinite point configurations and hence determines a random point process.
Keywords:
Big q-Jacobi polynomials, interpolation polynomials, symmetric functions, Schur functions, beta distribution.
Received: 24.01.2017 Accepted: 24.01.2017
Citation:
G. I. Olshanskii, “An analogue of the big $q$-Jacobi polynomials in the algebra of symmetric functions”, Funktsional. Anal. i Prilozhen., 51:3 (2017), 56–76; Funct. Anal. Appl., 51:3 (2017), 204–220
Linking options:
https://www.mathnet.ru/eng/faa3460https://doi.org/10.4213/faa3460 https://www.mathnet.ru/eng/faa/v51/i3/p56
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