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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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2011
Hauptverfasser: Vinet, L., Zhedanov, A.
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2011
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/146799
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren: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
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author Vinet, L.
Zhedanov, A.
author_facet Vinet, L.
Zhedanov, A.
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.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
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.
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2025-12-07T19:59:05Z
publishDate 2011
publisher Інститут математики НАН України
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
spellingShingle A Bochner Theorem for Dunkl Polynomials
Vinet, L.
Zhedanov, A.
title 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_short A Bochner Theorem for Dunkl Polynomials
title_sort bochner theorem for dunkl polynomials
url https://nasplib.isofts.kiev.ua/handle/123456789/146799
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