The Radon transform of Boehmians

Mikusiński, Piotr; Zayed, Ahmed

doi:10.1090/S0002-9939-1993-1145949-6

The Radon transform of Boehmians
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by Piotr Mikusiński and Ahmed Zayed PDF

Proc. Amer. Math. Soc. 118 (1993), 561-570 Request permission

Abstract:

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 several people including Gelfand, Graev, and Vilenkin, who extended it to tempered distributions. In this paper we extend the Radon transform to a space of Boehmians. Boehmians are defined as sequences of convolution quotients and include Schwartz distributions and regular Mikusiński operators. Our extension of the Radon transform includes generalized functions of infinite order with compact support. The technique used in this paper is based on algebraic properties of the Radon transform and its convolution structure rather than on their analytic properties. Our results do not contain nor are contained in those obtained by Gelfand et al.

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