Optimal recovery of linear operators in non-Euclidean metrics

Abstract

The paper is concerned with recovery problems of operators from noisy information in non-Euclidean metrics. A number of general theorems is put forward and applied to recovery problems of functions and their derivatives from noisy Fourier transform. In some cases, a family of optimal methods is found, from which the methods requiring the least amount of original information are singled out. Bibliography: 25 titles.