Paley-Wiener theorems for the Dunkl transform and Dunkl translation operators. (English) Zbl 1030.44004

Trimèche, Khalifa

Integral Transforms Spec. Funct. 13, No. 1, 17-38 (2002).

The author use the Dunkl intertwining operator \(V_k\) and its dual \(^tV_k\) [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.

Reviewer: S.L.Kalla (Kuwait)

MSC:

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

Keywords:

Dunkl intertwining operator; Paley-Wiener theorem; Dunkl transform; distributions; Dunkl translation operators; convolution product

Citations:

Zbl 0652.33004