Full C(N)D–research of the problem of recovery functions from the generalized Sobolev class

Abstract

In this paper a complete C(N)D-research of the problem of recovery functions from the generalized Sobolev class $W^{\omega_{r}}_{2}$ is carried out in the case, where numerical information of volume $N$ about the function $f$ being restored is removed from linear functionals. Namely, firstly, the exact order of error of restoring functions from classes $W^{\omega_{r}}_{2};$ is established in the metric $L^{q},2\leq q\leq \infty;$ secondly, a specific computing unit is proposed, that implements the exact order and its limiting error $\bar{\varepsilon}_{N}$ is found, that preserves the exact order and not improved in order; thirdly, it is proved that any computing unit constructed by the Fourier coefficients of the function being restored does not have a limiting error, better (in order) than $\bar{\varepsilon}_{N}.$