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Paley-Wiener theorems for the Dunkl transform and Dunkl translation operators. (English) Zbl 1030.44004
The author use the Dunkl intertwining operator ${V}_{k}$ and its dual ${}^{t}{V}_{k}$ [C. F. Dunkl, Trans. Am. Math. Soc. 311, 167-183 (1989; Zbl 0652.33004)] to establish a Paley-Wiener theorem for the Dunkl transform for functions, and distributions, and geometric forms of this theorem. These operators also permit to define and study Dunkl translation operators and convolution product.

MSC:
 44A15 Special transforms (Legendre, Hilbert, etc.) 44A35 Convolution (integral transforms) 46F12 Integral transforms in distribution spaces