Radon Transform of Distributions

Abstract

: In the literature there are three apparently different definitions of the Radon transform on various spaces of distributions: Gelfand-Graev’s, Helgason’s and Ludwig’s. In this paper a new definition of the Radon transform on the space of the tempered distributions is given and it is proved that, properly understood, the earlier definitions are all equivalent to the new one. A constructive description (a characterization) of the space of test functions is given. A simple method for studying the range of the Radon transform on some spaces of distributions is described.