Hankel type transform on a Gevrey type space

Abstract

In this paper we give a completion for the distributional theory of Hankel type transformation developed in [6] and [8]. The space H_w generalizing the Altenburg space H is defined. Some properties of this space are studied. It is shown that the Hankel type transformation h a,b is an automorphism of H_w . The generalized Hankel type transform of Gevrey spaces is defined and it is found that Hankel transform is an automorphism of H_w′. Product on H_w, Hankel type translation and Hankel type convolution on _Hw are investigated.