A Bochner Theorem for Dunkl Polynomials
We establish an analogue of the Bochner theorem for first order operators of Dunkl type, that is we classify all such operators having polynomial solutions. Under natural conditions it is seen that the only families of orthogonal polynomials in this category are limits of little and big q-Jacobi pol...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2011 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2011
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146799 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | A Bochner Theorem for Dunkl Polynomials / L. Vinet, A. Zhedanov // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 16 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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Vinet, L. Zhedanov, A. 2019-02-11T15:24:30Z 2019-02-11T15:24:30Z 2011 A Bochner Theorem for Dunkl Polynomials / L. Vinet, A. Zhedanov // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 16 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 33C45; 33C47; 42C05 DOI:10.3842/SIGMA.2011.020 https://nasplib.isofts.kiev.ua/handle/123456789/146799 We establish an analogue of the Bochner theorem for first order operators of Dunkl type, that is we classify all such operators having polynomial solutions. Under natural conditions it is seen that the only families of orthogonal polynomials in this category are limits of little and big q-Jacobi polynomials as q=−1. This paper is a contribution to the Special Issue “Symmetry, Separation, Super-integrability and Special Functions (S4)”. The full collection is available at http://www.emis.de/journals/SIGMA/S4.html. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A Bochner Theorem for Dunkl Polynomials Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
A Bochner Theorem for Dunkl Polynomials |
| spellingShingle |
A Bochner Theorem for Dunkl Polynomials Vinet, L. Zhedanov, A. |
| title_short |
A Bochner Theorem for Dunkl Polynomials |
| title_full |
A Bochner Theorem for Dunkl Polynomials |
| title_fullStr |
A Bochner Theorem for Dunkl Polynomials |
| title_full_unstemmed |
A Bochner Theorem for Dunkl Polynomials |
| title_sort |
bochner theorem for dunkl polynomials |
| author |
Vinet, L. Zhedanov, A. |
| author_facet |
Vinet, L. Zhedanov, A. |
| publishDate |
2011 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We establish an analogue of the Bochner theorem for first order operators of Dunkl type, that is we classify all such operators having polynomial solutions. Under natural conditions it is seen that the only families of orthogonal polynomials in this category are limits of little and big q-Jacobi polynomials as q=−1.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/146799 |
| citation_txt |
A Bochner Theorem for Dunkl Polynomials / L. Vinet, A. Zhedanov // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 16 назв. — англ. |
| work_keys_str_mv |
AT vinetl abochnertheoremfordunklpolynomials AT zhedanova abochnertheoremfordunklpolynomials AT vinetl bochnertheoremfordunklpolynomials AT zhedanova bochnertheoremfordunklpolynomials |
| first_indexed |
2025-12-07T19:59:05Z |
| last_indexed |
2025-12-07T19:59:05Z |
| _version_ |
1850880867168157696 |