On Recovery of the Singular Differential Laplace—Bessel Operator from the Fourier–Bessel Transform
Sergey M. Sitnik,
Vladimir E. Fedorov,
Marina V. Polovinkina,
Igor P. Polovinkin
Affiliations
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
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.
