In this paper we give a completion for the distributional theory of Hankel type transformation developed in  and . The space Hw generalizing the Altenburg space H is defined. Some properties of this space are studied. It is shown that the Hankel type transformation hα,β is an automorphism of Hw . The generalized Hankel type transform of Gevrey spaces is defined and it is found that Hankel transform is an automorphism of Hw' . Product on Hw, Hankel type translation and Hankel type convolution on Hw are investigated.
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