Harmonic analysis associated with the Cherednik operators and the Heckman-Opdam theory. (English) Zbl 1207.33024

Summary: By using the trigonometric Dunkl intertwining operator and its dual introduced by the author in [Adv. Pure Appl. Math. (to appear)], we define and study the hypergeometric translation operators associated with the Cherednik operators \(T_j\), \(j=1,2,\dots,d\). Next with the help of these translation operators, we define and study the hypergeometric convolution product of functions and distributions associated with the operators \(T_j\), \(j=1,2,\dots,d\).


33E30 Other functions coming from differential, difference and integral equations
33C67 Hypergeometric functions associated with root systems
42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
43A32 Other transforms and operators of Fourier type
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