Radon transforms of tempered distributions (Q1772951)

The author very beautifully discusses the convergence problem of Radon transforms for the space of tempered distributions. This is a good departure from defining integral transforms unscrupulously (without discussing convergence etc.). We refer the reader to [\textit{J.~M.~C.\ Joshi}, ``Fractional integration and certain integral transforms'', Agra University Journal of Research (Sc.) 15 (1966)], where the reviewer rigorously discussed the convergence and other problems for S.~M.\ Joshi's generalized Laplace transform \[ (S^a_b f) (x)= {\Gamma(a)\over\Gamma(b)} {_1F_1} (a; b; -xy)\, f(y)\,dy, \] which was later on extended to distributions by him [see also \textit{J. M. C. Joshi}, Integral Transforms Spec. Funct. 15, No.~2, 117--127 (2004; Zbl 1063.44004)].