A Probablistic Origin for a New Class of Bivariate Polynomials

We present here a probabilistic approach to the generation of new polynomials in two discrete variables. This extends our earlier work on the 'classical' orthogonal polynomials in a previously unexplored direction, resulting in the discovery of an exactly soluble eigenvalue problem corresp...

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Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2008
Автори: Hoare, M.R., Rahman, M.
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2008
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/148000
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:A Probablistic Origin for a New Class of Bivariate Polynomials / M.R. Hoare, M. Rahman // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 24 назв. — англ.

Репозитарії

Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-148000
record_format dspace
spelling Hoare, M.R.
Rahman, M.
2019-02-16T16:24:26Z
2019-02-16T16:24:26Z
2008
A Probablistic Origin for a New Class of Bivariate Polynomials / M.R. Hoare, M. Rahman // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 24 назв. — англ.
1815-0659
2000 Mathematics Subject Classification: 33C45; 60J05
https://nasplib.isofts.kiev.ua/handle/123456789/148000
We present here a probabilistic approach to the generation of new polynomials in two discrete variables. This extends our earlier work on the 'classical' orthogonal polynomials in a previously unexplored direction, resulting in the discovery of an exactly soluble eigenvalue problem corresponding to a bivariate Markov chain with a transition kernel formed by a convolution of simple binomial and trinomial distributions. The solution of the relevant eigenfunction problem, giving the spectral resolution of the kernel, leads to what we believe to be a new class of orthogonal polynomials in two discrete variables. Possibilities for the extension of this approach are discussed.
This paper is a contribution to the Special Issue on Dunkl Operators and Related Topics.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
A Probablistic Origin for a New Class of Bivariate Polynomials
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title A Probablistic Origin for a New Class of Bivariate Polynomials
spellingShingle A Probablistic Origin for a New Class of Bivariate Polynomials
Hoare, M.R.
Rahman, M.
title_short A Probablistic Origin for a New Class of Bivariate Polynomials
title_full A Probablistic Origin for a New Class of Bivariate Polynomials
title_fullStr A Probablistic Origin for a New Class of Bivariate Polynomials
title_full_unstemmed A Probablistic Origin for a New Class of Bivariate Polynomials
title_sort probablistic origin for a new class of bivariate polynomials
author Hoare, M.R.
Rahman, M.
author_facet Hoare, M.R.
Rahman, M.
publishDate 2008
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
description We present here a probabilistic approach to the generation of new polynomials in two discrete variables. This extends our earlier work on the 'classical' orthogonal polynomials in a previously unexplored direction, resulting in the discovery of an exactly soluble eigenvalue problem corresponding to a bivariate Markov chain with a transition kernel formed by a convolution of simple binomial and trinomial distributions. The solution of the relevant eigenfunction problem, giving the spectral resolution of the kernel, leads to what we believe to be a new class of orthogonal polynomials in two discrete variables. Possibilities for the extension of this approach are discussed.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/148000
citation_txt A Probablistic Origin for a New Class of Bivariate Polynomials / M.R. Hoare, M. Rahman // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 24 назв. — англ.
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