Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2021, Volume 193, Pages 104–109
DOI: https://doi.org/10.36535/0233-6723-2021-193-104-109 (Mi into804) 		 
An analog of the Paley–Wiener theorem for the Radon $K_\gamma$-transform for integer $|\gamma|$

L. N. Lyakhova, M. G. Lapshinab

a Voronezh State University
b Lipetsk State Pedagogical University
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DOI: https://doi.org/10.36535/0233-6723-2021-193-104-109
Abstract: The study of the Radon transformation based on weighted plane waves was initiated by I. A. Kipriyanov. In this paper, we obtain necessary and sufficient conditions satisfied by the Radon $K_\gamma$-transform of smooth functions that decrease together with all their derivatives.
Keywords: Paley–Wiener theorem, Radon transform, Radon–Kipriyanov transform, inversion of the Radon transform, inversion of the Radon–Kipriyanov transform.
Bibliographic databases:
Document Type: Article
UDC: 517.44
MSC: 44A12, 42A38
Language: Russian
Citation: L. N. Lyakhov, M. G. Lapshina, “An analog of the Paley–Wiener theorem for the Radon $K_\gamma$-transform for integer $|\gamma|$”, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 4, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 193, VINITI, Moscow, 2021, 104–109
Citation in format AMSBIB
\Bibitem{LyaLap21}
\by L.~N.~Lyakhov, M.~G.~Lapshina
\paper An analog of the Paley--Wiener theorem for the Radon $K_\gamma$-transform for integer $|\gamma|$
\inbook Proceedings of the Voronezh spring mathematical school
“Modern methods of the theory of boundary-value problems. Pontryagin
readings – XXX”.
Voronezh, May 3-9, 2019. Part 4
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2021
\vol 193
\pages 104--109
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into804}
\crossref{https://doi.org/10.36535/0233-6723-2021-193-104-109}
\elib{https://elibrary.ru/item.asp?id=46666139}
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