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

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5 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)204-220
Number of pages17
JournalFunctional Analysis and its Applications
Volume51
Issue number3
DOIs
Publication statusPublished - 1 Jul 2017

Keywords

  • beta distribution
  • Big q-Jacobi polynomials
  • interpolation polynomials
  • Schur functions
  • symmetric functions

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