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
Date:2011
Main Authors: Vinet, L., Zhedanov, A.
Format: Article
Language:English
Published: Інститут математики НАН України 2011
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 nasplib_isofts_kiev_ua-123456789-146799
record_format dspace
spelling 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.
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AT zhedanova abochnertheoremfordunklpolynomials
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first_indexed 2025-12-07T19:59:05Z
last_indexed 2025-12-07T19:59:05Z
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