An Alternative Definition of the Hermite Polynomials Related to the Dunkl Laplacian
| dc.creator | De Bie, Hendrik | |
| dc.date | 2008-12-28 | |
| dc.date.accessioned | 2026-07-07T12:22:57Z | |
| dc.date.available | 2026-07-07T12:22:57Z | |
| dc.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 $L^{2}$ space introduced by Dunkl. | |
| dc.description | This is a contribution to the Special Issue on Dunkl Operators and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/ | |
| dc.identifier | https://arxiv.org/abs/0812.4819 | |
| dc.identifier | http://arxiv.org/abs/0812.4819 | |
| dc.identifier | SIGMA 4 (2008), 093, 11 pages | |
| dc.identifier | doi:10.3842/SIGMA.2008.093 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/213831 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Mathematical Physics | |
| dc.title | An Alternative Definition of the Hermite Polynomials Related to the Dunkl Laplacian | |
| dc.type | text |