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The trigonometric Dunkl intertwining operator and its dual associated with the Cherednik operators and the Heckman–Opdam theory
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Khalifa Trimèche
Published/Copyright:
May 7, 2010
Abstract
In this paper we prove that there exists a unique topological isomorphism Vk from 
(the space of C∞-functions on 
) onto itself which intertwines the Cherednik operators Tj, j = 1, 2, . . . , d, and the partial derivatives 
, j = 1, 2, . . . , d, called the trigonometric Dunkl intertwining operator (this name has been proposed by G. J. Heckman). To define and study the operator Vk we have introduced first the trigonometric Dunkl dual intertwining operator tVk. The operators Vk and tVk are the analogue in the Dunkl theory of the Dunkl intertwining operator and its dual (see [Dunkl, Can. J. Math. 43: 1213–1227, 1991, Trimèche, Integrals Transforms Special Funct. 12: 349–374, 2001]).
Keywords.: Cherednik operators; Heckman–Opdam theory; trigonometric Dunkl intertwining operator and its dual; hypergeometric Fourier transform
Received: 2008-11-06
Revised: 2009-05-15
Published Online: 2010-05-07
Published in Print: 2010-September
© de Gruyter 2010
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Articles in the same Issue
- The trigonometric Dunkl intertwining operator and its dual associated with the Cherednik operators and the Heckman–Opdam theory
- β-Jacobi processes
- On Laguerre–Hahn linear functionals: the symmetric companion
- On a generalization of Kantorovich operators on simplices and hypercubes
- Existence of solutions for anisotropic quasilinear elliptic equations with variable exponent
Keywords for this article
Cherednik operators;
Heckman–Opdam theory;
trigonometric Dunkl intertwining operator and its dual;
hypergeometric Fourier transform
Articles in the same Issue
- The trigonometric Dunkl intertwining operator and its dual associated with the Cherednik operators and the Heckman–Opdam theory
- β-Jacobi processes
- On Laguerre–Hahn linear functionals: the symmetric companion
- On a generalization of Kantorovich operators on simplices and hypercubes
- Existence of solutions for anisotropic quasilinear elliptic equations with variable exponent
