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Sibirskii Zhurnal Industrial'noi Matematiki, 2024, Volume 27, Number 3, Pages 5–11
DOI: https://doi.org/10.33048/SIBJIM.2024.27.301 (Mi sjim1286) 		 
Radon transform inversion formula in the class of discontinuous functions

D. S. Anikonov, D. S. Konovalova

Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
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DOI: https://doi.org/10.33048/SIBJIM.2024.27.301
Abstract: We introduce the concept of a pseudoconvex set in an odd-dimensional Euclidean space. The inversion formula is obtained for the Radon transform in the case where the integrand is a piecewise continuous function defined on a pseudoconvex set. The result achieved is a generalization of a previously known property proved for smooth functions.
Keywords: Radon transform, discontinuous functions, pseudoconvex set, probing, tomography, inversion formula.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0009
Received: 04.07.2023
Revised: 18.04.2024
Accepted: 22.05.2024
English version:
Journal of Applied and Industrial Mathematics, 2024, Volume 18, Issue 3, Pages 379–383
DOI: https://doi.org/10.1134/S1990478924030013
Document Type: Article
UDC: 517.44
Language: Russian
Citation: D. S. Anikonov, D. S. Konovalova, “Radon transform inversion formula in the class of discontinuous functions”, Sib. Zh. Ind. Mat., 27:3 (2024), 5–11; J. Appl. Industr. Math., 18:3 (2024), 379–383
Citation in format AMSBIB
\Bibitem{AniKon24}
\by D.~S.~Anikonov, D.~S.~Konovalova
\paper Radon transform inversion formula in the class of discontinuous functions
\jour Sib. Zh. Ind. Mat.
\yr 2024
\vol 27
\issue 3
\pages 5--11
\mathnet{http://mi.mathnet.ru/sjim1286}
\crossref{https://doi.org/10.33048/SIBJIM.2024.27.301}
\transl
\jour J. Appl. Industr. Math.
\yr 2024
\vol 18
\issue 3
\pages 379--383
\crossref{https://doi.org/10.1134/S1990478924030013}
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    		Сибирский журнал индустриальной математики
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