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arXiv · 0812.4819

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

Hendrik De Bie
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Abstract

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.

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Hendrik De Bie. 2008-12-28. An Alternative Definition of the Hermite Polynomials Related to the Dunkl Laplacian. https://doi.org/10.3842/sigma.2008.093

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