Distributional Fourier Transform and Convolution Associated to Chébli-Trimèche Hypergroups

 In this paper we investigate the convolution and the generalized Fourier transform related to Chébli-Trimèche hypergroups on new spaces of distributions. Boundedness, smoothness, uniqueness, and inversion theorems are established for this transform, as well as the main properties of the convolution. The theory developed is used in solving a differential equation involving a singular differential operator.