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Harmonic analysis associated with the Cherednik operators and the Heckman–Opdam theory
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Khalifa Trimèche
Published/Copyright:
February 2, 2011
Abstract
By using the trigonometric Dunkl intertwining operator and its dual introduced by the author in [Trimèche, Adv. Pure Appl. Math.], we define and study the hypergeometric translation operators associated with the Cherednik operators Tj, j = 1, 2, . . . , d. Next with the help of these translation operators, we define and study the hypergeometric convolution product of functions and distributions associated with the operators Tj, j = 1, 2, . . . , d.
Keywords.: Cherednik operators; Heckman–Opdam theory; trigonometric Dunkl intertwining operator and its dual; hypergeometric Fourier transform; hypergeometric translation operators; hypergeometric convolution product
Received: 2008-11-06
Revised: 2009-05-11
Published Online: 2011-02-02
Published in Print: 2011-January
© de Gruyter 2011
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Articles in the same Issue
- Weighted Lp-solutions on unbounded intervals of nonlinear integral equations of the Hammerstein and Urysohn types
- Harmonic analysis associated with the Cherednik operators and the Heckman–Opdam theory
- Solutions to conjugate Beltrami equations and approximation in generalized Hardy spaces
- Toeplitz operators with L1 symbols on Bergman spaces in the unit ball of
- On the boundedness of pseudo-differential operators associated with the Dunkl transform on the real line
- Equivalences induced by n-self-cotilting comodules
