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- Title
Clifford-Gegenbauer polynomials related to the Dunkl Dirac operator.
- Authors
de Bie, H.; de Schepper, N.
- Abstract
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 ℝm. In both cases we obtain several properties of these polynomials, such as a Rodrigues formula, a differential equation and an explicit relation connecting themwith the Jacobi polynomials on the real line. As in the classical Clifford case, the orthogonality of the polynomials on ℝm must be treated in a completely different way than the orthogonality of their counterparts on B(1). In case of ℝm, 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.
- Subjects
POLYNOMIALS; JACOBI polynomials; EUCLIDEAN algorithm; DIFFERENTIAL equations; BILINEAR forms
- Publication
Bulletin of the Belgian Mathematical Society - Simon Stevin, 2011, Vol 18, Issue 2, p193
- ISSN
1370-1444
- Publication type
Article
- DOI
10.36045/bbms/1307452070