The n-Dimensional Distributional Hankel Transformation

Abstract

The Hankel transformation was extended to certain generalized functions of one dimension [1; 2; 3]. In this paper, we develop the n-dimensional case corresponding to [1]. The procedure in [1] is briefly as follows:A test function space Hμ is constructed on which the μth order Hankel transformation hμ defined byis an automorphism whenever μ ≧ —1/2. The generalized transformation hμ' is then defined on the dual Hμ' as the adjoint of hμ through a Parseval relation, i.e.