Clifford-Gegenbauer polynomials related to the Dunkl Dirac operator

Autor:	De Bie, H., De Schepper, N.
Rok vydání:	2010
Předmět:	Mathematics - Classical Analysis and ODEs Mathematics - Complex Variables 30G35 33C80 33C45
Druh dokumentu:	Working Paper
Popis:	We introduce the so-called Clifford-Gegenbauer polynomials in the framework of Dunkl operators, as well on the unit ball B(1), as on the Euclidean space $R^m$. In both cases we obtain several properties of these polynomials, such as a Rodrigues formula, a differential equation and an explicit relation connecting them with the Jacobi polynomials on the real line. As in the classical Clifford case, the orthogonality of the polynomials on $R^m$ must be treated in a completely different way than the orthogonality of their counterparts on B(1). In case of $R^m$, it must be expressed in terms of a bilinear form instead of an integral. Furthermore, in this paper the theory of Dunkl monogenics is further developed. Comment: 19 pages, accepted for publication in Bulletin of the BMS
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1003.1512 Zobrazit plný text záznamu View this record from Arxiv