An Alternative Definition of the Hermite Polynomials Related to the Dunkl Laplacian

We introduce the so-called Clifford-Hermite polynomials in the framework of Dunkl operators, based on the theory of Clifford analysis. Several properties of these polynomials are obtained, such as a Rodrigues formula, a differential equation and an explicit relation connecting them with the generali...

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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2008
1. Verfasser: De Bie, H.
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2008
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/147996
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:An Alternative Definition of the Hermite Polynomials Related to the Dunkl Laplacian / H. De Bie // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 24 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author De Bie, H.
author_facet De Bie, H.
citation_txt An Alternative Definition of the Hermite Polynomials Related to the Dunkl Laplacian / H. De Bie // 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 introduce the so-called Clifford-Hermite polynomials in the framework of Dunkl operators, based on the theory of Clifford analysis. Several properties of these polynomials are obtained, such as a Rodrigues formula, a differential equation and an explicit relation connecting them with the generalized Laguerre polynomials. A link is established with the generalized Hermite polynomials related to the Dunkl operators (see [Rösler M., Comm. Math. Phys. 192 (1998), 519-542, q-alg/9703006.]) as well as with the basis of the weighted L2 space introduced by Dunkl.
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2025-12-07T18:38:00Z
publishDate 2008
publisher Інститут математики НАН України
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spelling De Bie, H.
2019-02-16T16:20:44Z
2019-02-16T16:20:44Z
2008
An Alternative Definition of the Hermite Polynomials Related to the Dunkl Laplacian / H. De Bie // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 24 назв. — англ.
1815-0659
2000 Mathematics Subject Classification: 33C80; 33C45; 30G35
https://nasplib.isofts.kiev.ua/handle/123456789/147996
We introduce the so-called Clifford-Hermite polynomials in the framework of Dunkl operators, based on the theory of Clifford analysis. Several properties of these polynomials are obtained, such as a Rodrigues formula, a differential equation and an explicit relation connecting them with the generalized Laguerre polynomials. A link is established with the generalized Hermite polynomials related to the Dunkl operators (see [Rösler M., Comm. Math. Phys. 192 (1998), 519-542, q-alg/9703006.]) as well as with the basis of the weighted L2 space introduced by Dunkl.
This paper is a contribution to the Special Issue on Dunkl Operators and Related Topics. The author is supported by a Ph.D. Fellowship of the the Research Foundation - Flanders (FWO).
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Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
An Alternative Definition of the Hermite Polynomials Related to the Dunkl Laplacian
Article
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spellingShingle An Alternative Definition of the Hermite Polynomials Related to the Dunkl Laplacian
De Bie, H.
title An Alternative Definition of the Hermite Polynomials Related to the Dunkl Laplacian
title_full An Alternative Definition of the Hermite Polynomials Related to the Dunkl Laplacian
title_fullStr An Alternative Definition of the Hermite Polynomials Related to the Dunkl Laplacian
title_full_unstemmed An Alternative Definition of the Hermite Polynomials Related to the Dunkl Laplacian
title_short An Alternative Definition of the Hermite Polynomials Related to the Dunkl Laplacian
title_sort alternative definition of the hermite polynomials related to the dunkl laplacian
url https://nasplib.isofts.kiev.ua/handle/123456789/147996
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AT debieh alternativedefinitionofthehermitepolynomialsrelatedtothedunkllaplacian