On Recovery of the Singular Differential Laplace—Bessel Operator from the Fourier–Bessel Transform

Sergey M. Sitnik (), Vladimir E. Fedorov, Marina V. Polovinkina and Igor P. Polovinkin
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Sergey M. Sitnik: Department of Applied Mathematics and Computer Modeling, Belgorod State National Research University (BelGU), Pobedy St., 85, 308015 Belgorod, Russia
Vladimir E. Fedorov: Department of Mathematical Analysis, Chelyabinsk State University, 129, Kashirin Brothers St., 454001 Chelyabinsk, Russia
Marina V. Polovinkina: Department of Higher Mathematics and Information Technologies, Voronezh State University of Engineering Technologies, Revolution Av., 19, 394036 Voronezh, Russia
Igor P. Polovinkin: Department of Applied Mathematics and Computer Modeling, Belgorod State National Research University (BelGU), Pobedy St., 85, 308015 Belgorod, Russia

Mathematics, 2023, vol. 11, issue 5, 1-16

Abstract: This paper is devoted to the problem of the best recovery of a fractional power of the B-elliptic operator of a function on R + N by its Fourier–Bessel transform known approximately on a convex set with the estimate of the difference between Fourier–Bessel transform of the function and its approximation in the metric L ∞ . The optimal recovery method has been found. This method does not use the Fourier–Bessel transform values beyond a ball centered at the origin.

Keywords: Bessel operator; extremal problem; optimal recovery; Fourier–Bessel transform (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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