An analogue of the big q-Jacobi polynomials in the algebra of symmetric functions

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 resu...

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Bibliographic Details
Published in:Functional analysis and its applications 2017-07, Vol.51 (3), p.204-220
Main Author: Olshanski, G. I.
Format: Article
Language:English
Subjects:
Analysis
Functional Analysis
Functions (mathematics)
Mathematical analysis
Mathematics
Mathematics and Statistics
Polynomials
Well construction
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Summary: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.
ISSN:0016-2663
1573-8485
DOI:10.1007/s10688-017-0184-1