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...
Gespeichert in:
| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2008 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2008
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/148000 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862748814813691904 |
|---|---|
| author | Hoare, M.R. Rahman, M. |
| author_facet | Hoare, M.R. Rahman, M. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
|
| first_indexed | 2025-12-07T20:57:23Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148000 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T20:57:23Z |
| publishDate | 2008 |
| publisher | Інститут математики НАН України |
| 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 |
| spellingShingle | A Probablistic Origin for a New Class of Bivariate Polynomials Hoare, M.R. Rahman, M. |
| title | 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_short | A Probablistic Origin for a New Class of Bivariate Polynomials |
| title_sort | probablistic origin for a new class of bivariate polynomials |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148000 |
| work_keys_str_mv | AT hoaremr aprobablisticoriginforanewclassofbivariatepolynomials AT rahmanm aprobablisticoriginforanewclassofbivariatepolynomials AT hoaremr probablisticoriginforanewclassofbivariatepolynomials AT rahmanm probablisticoriginforanewclassofbivariatepolynomials |