Geodesic
Recovery of the Laplace--Bessel operator of a function by the spectrum, which is specified not everywhere
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international winter mathematical school "Modern methods of function theory and related problems", Voronezh, January 27 - February 1, 2023, Part 2, Tome 228 (2023), pp. 52-57

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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
Mots-clés : Fourier–Bessel transform 
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     author = {S. M. Sitnik and M. V. Polovinkina and V. E. Fedorov and I. P. Polovinkin},
     title = {Recovery of the {Laplace--Bessel} operator of a function by the spectrum, which is specified not everywhere},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {52--57},
     publisher = {mathdoc},
     volume = {228},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2023_228_a4/}
}
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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. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international winter mathematical school "Modern methods of function theory and related problems", Voronezh, January 27 - February 1, 2023, Part 2, Tome 228 (2023), pp. 52-57. http://geodesic.mathdoc.fr/item/INTO_2023_228_a4/