THE RADON-TRANSFORM OF BOHEMIANS

The Radon transform, which enables one to reconstruct a function of N variables from the knowledge of its integrals over all hyperplanes of dimension N - 1 , has been extended to Schwartz distributions by sever al people including Gelfand, Graev, and Vilenkin, who extended it to t empered distributions. In this paper we extend the Radon transform to a space of Boehmians. Boehmians are defined as sequences of convolutio n quotients and include Schwartz distributions and regular Mikusinski operators. Our extension of the Radon transform includes generalized f unctions of infinite order with compact support. The technique used in this paper is based on algebraic properties of the Radon transform an d its convolution structure rather than on their analytic properties. Our results do not contain nor are contained in those obtained by Gelf and et al.