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

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.