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Funktsional. Anal. i Prilozhen., 2017, Volume 51, Issue 3, Pages 56–76 (Mi faa3460)  

This article is cited in 2 scientific papers (total in 3 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.

Funding Agency Grant Number
Russian Science Foundation 14-50-00150
The present research was carried out at the Institute for Information Transmission Problems of the Russian Academy of Sciences at the expense of the Russian Science Foundation (project no. 14-50-00150).


DOI: https://doi.org/10.4213/faa3460

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English version:
Functional Analysis and Its Applications, 2017, 51:3, 204–220

Bibliographic databases:

UDC: 517.587+517.588
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

Citation in format AMSBIB
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\paper An analogue of the big $q$-Jacobi polynomials in the algebra of symmetric functions
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. C. Cuenca, “Interpolation Macdonald operators at infinity”, Adv. in Appl. Math., 101 (2018), 15–59  crossref  mathscinet  zmath  isi  scopus
    2. G. Olshanski, “Interpolation Macdonald polynomials and Cauchy-type identities”, J. Combin. Theory Ser. A, 162 (2019), 65–117  crossref  mathscinet  zmath  isi  scopus
    3. A. M. Borodin, Aleksandr I. Bufetov, Aleksei I. Bufetov, A. M. Vershik, V. E. Gorin, A. I. Molev, V. F. Molchanov, R. S. Ismagilov, A. A. Kirillov, M. L. Nazarov, Yu. A. Neretin, N. I. Nessonov, A. Yu. Okounkov, L. A. Petrov, S. M. Khoroshkin, “Grigori Iosifovich Olshanski (on his 70th birthday)”, Russian Math. Surveys, 74:3 (2019), 555–577  mathnet  crossref  crossref  adsnasa  isi  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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