Title

The Radon Transform Of Boehmians

Keywords

Boehmians; Generalized functions; Radon transform

Abstract

The Radon transform, which enables one to reconstructa 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. © 1993 American Mathematical Society.

Publication Date

1-1-1993

Publication Title

Proceedings of the American Mathematical Society

Volume

118

Issue

2

Number of Pages

561-570

Document Type

Article

Identifier

scopus

Personal Identifier

scopus

DOI Link

https://doi.org/10.1090/S0002-9939-1993-1145949-6

Socpus ID

84966259596 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84966259596

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