The Radon-Transform Of Bohemians

    Authors

    P. Mikusinski;A. Zayed

    Comments

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    Abbreviated Journal Title

    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.

    Journal 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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