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
Recommended Citation
Ournycheva, E., & Rubin, B. (2008). Semyanistyi's integrals and radon transforms on matrix spaces. Journal of Fourier Analysis and Applications, 14 (1), 60-88. https://doi.org/10.1007/s00041-007-9002-0