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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| Дата: | 2011 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2011
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146799 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | A Bochner Theorem for Dunkl Polynomials / L. Vinet, A. Zhedanov // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 16 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-146799 |
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| record_format |
dspace |
| spelling |
irk-123456789-1467992019-02-12T01:23:51Z A Bochner Theorem for Dunkl Polynomials Vinet, L. Zhedanov, A. 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. 2011 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/146799 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Vinet, L. Zhedanov, A. |
| spellingShingle |
Vinet, L. Zhedanov, A. A Bochner Theorem for Dunkl Polynomials Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Vinet, L. Zhedanov, A. |
| author_sort |
Vinet, L. |
| title |
A Bochner Theorem for Dunkl Polynomials |
| 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 |
| publisher |
Інститут математики НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT vinetl abochnertheoremfordunklpolynomials AT zhedanova abochnertheoremfordunklpolynomials AT vinetl bochnertheoremfordunklpolynomials AT zhedanova bochnertheoremfordunklpolynomials |
| first_indexed |
2023-05-20T17:25:50Z |
| last_indexed |
2023-05-20T17:25:50Z |
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1796153275465072640 |