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. 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.
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Communicated by Fulvio Ricci.
The authors were supported in part by the Edmund Landau Center for Research in Mathematical Analysis and Related Areas, sponsored by the Minerva Foundation (Germany). The first author was also supported by Abraham and Sarah Gelbart Research Institute for Mathematical Sciences. The second author was also supported by the NSF grants EPS-0346411 (Louisiana Board of Regents) and DMS-0556157).
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Ournycheva, E., Rubin, B. Semyanistyi’s Integrals and Radon Transforms on Matrix Spaces. J Fourier Anal Appl 14, 60–88 (2008). https://doi.org/10.1007/s00041-007-9002-0
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DOI: https://doi.org/10.1007/s00041-007-9002-0