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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2008 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2008
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| Онлайн доступ: | 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 |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862722736420290560 |
|---|---|
| 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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| first_indexed | 2025-12-07T18:38:00Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147996 |
| 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 |
| record_format | dspace |
| 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). 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 |
| 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 |
| work_keys_str_mv | AT debieh analternativedefinitionofthehermitepolynomialsrelatedtothedunkllaplacian AT debieh alternativedefinitionofthehermitepolynomialsrelatedtothedunkllaplacian |