Semyanistyi's integrals and radon transforms on matrix spaces

Document Type

Article

Publication Date

2-1-2008

Abstract

We introduce a new analytic family of intertwining operators which include the Radon transform over matrix planes and its inverse. These operators generalize integral transformations introduced by Semyanistyi (Dokl. Akad. Nauk SSSR 134:536-539, [1960]) in his research related to the hyperplane Radon transform in ℝn n . We obtain an extended version of Fuglede's formula, connecting generalized Semyanistyi's integrals, Radon transforms and Riesz potentials on the space of real rectangular matrices. This result combined with the matrix analog of the Hilbert transform leads to variety of new explicit inversion formulas for the Radon transform of functions of matrix argument. © 2008 Birkhäuser Boston.

Publication Source (Journal or Book title)

Journal of Fourier Analysis and Applications

First Page

60

Last Page

88

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