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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2008 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2008
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147996 |
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| Cite this: | 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| id |
nasplib_isofts_kiev_ua-123456789-147996 |
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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). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications An Alternative Definition of the Hermite Polynomials Related to the Dunkl Laplacian Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
An Alternative Definition of the Hermite Polynomials Related to the Dunkl Laplacian |
| spellingShingle |
An Alternative Definition of the Hermite Polynomials Related to the Dunkl Laplacian De Bie, H. |
| title_short |
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_sort |
alternative definition of the hermite polynomials related to the dunkl laplacian |
| author |
De Bie, H. |
| author_facet |
De Bie, H. |
| publishDate |
2008 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| 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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/147996 |
| 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. |
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2025-12-07T18:38:00Z |
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2025-12-07T18:38:00Z |
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