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

• 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
• 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.

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...