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

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 approximati...

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Bibliographic Details
Published in:Mathematics (Basel) 2023-03, Vol.11 (5), p.1103
Main Authors: Sitnik, Sergey M., Fedorov, Vladimir E., Polovinkina, Marina V., Polovinkin, Igor P.
Format: Article
Language:English
Subjects:
Approximation
Bessel operator
Convexity
Euclidean space
extremal problem
Fourier transforms
Fourier–Bessel transform
Laplacian operator
Mathematical research
Operators (mathematics)
optimal recovery
Recovery
Transformations (Mathematics)
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11051103