Title

The Radon-Transform Of Bohemians

Title - Alternative

Proc. Amer. Math. Soc.

Keywords

Radon Transform; Bohemians; Generalized Functions; Mathematics, Applied; Mathematics

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 Mikusinski 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.

Publication Title

Proceedings of the American Mathematical Society

Volume

118

Issue/Number

2

Publication Date

1-1-1993

Document Type

Article

Language

English

First Page

561

Last Page

570

WOS Identifier

WOS:A1993LD52000035

ISSN

0002-9939

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