Optimal Recovery of Functions from Inaccurate Data on the Radon Transform for Classes Defined by the Degree of the Laplacian

Abstract

We consider the problem of optimal recovery of function in Schwartz space from inaccurate data (in the mean square metric) on it’s Radon transform. We present explicit expressions for the error of optimal recovery and a set of optimal methods. As a consequence we prove one inequality for functions in Schwartz space.