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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2023, Volume 228, Pages 52–57
DOI: https://doi.org/10.36535/0233-6723-2023-228-52-57 (Mi into1226) 		 
Recovery of the Laplace–Bessel operator of a function by the spectrum, which is specified not everywhere

S. M. Sitnika, M. V. Polovinkinab, V. E. Fedorovcd, I. P. Polovinkina

a National Research University "Belgorod State University"
b Voronezh State University of Engineering Technologies
c N.N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
d Chelyabinsk State University
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DOI: https://doi.org/10.36535/0233-6723-2023-228-52-57
Abstract: In this paper, we present results related to the problem of the best recovery of a fractional power of the $B$-elliptic Laplace–Bessel operator of a smooth function from its Fourier–Bessel transform, which is known exactly or approximately on a certain convex set. The cases of primary estimates in $L_2^\gamma$ and $L_\infty$ are considered.
Keywords: Bessel operator, optimal recovery, extremal problem, Fourier–Bessel transform
Document Type: Article
UDC: 517.444, 517.9
MSC: 26A33, 35Q92, 35B40, 43A32, 35J15
Language: Russian
Citation: S. M. Sitnik, M. V. Polovinkina, V. E. Fedorov, I. P. Polovinkin, “Recovery of the Laplace–Bessel operator of a function by the spectrum, which is specified not everywhere”, Proceedings of the Voronezh international winter mathematical school "Modern methods of function theory and related problems", Voronezh, January 27 - February 1, 2023, Part 2, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 228, VINITI, Moscow, 2023, 52–57
Citation in format AMSBIB
\Bibitem{SitPolFed23}
\by S.~M.~Sitnik, M.~V.~Polovinkina, V.~E.~Fedorov, I.~P.~Polovinkin
\paper Recovery of the Laplace--Bessel operator of a function by the spectrum, which is specified not everywhere
\inbook Proceedings of the Voronezh international winter mathematical school "Modern methods of function theory and related problems", Voronezh, January 27 - February 1, 2023, Part 2
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2023
\vol 228
\pages 52--57
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into1226}
\crossref{https://doi.org/10.36535/0233-6723-2023-228-52-57}
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