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: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2008
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| 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
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nasplib_isofts_kiev_ua-123456789-148000 |
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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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2025-12-07T20:57:23Z |
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2025-12-07T20:57:23Z |
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