Optimal recovery of functions from anisotropic Sobolev classes on a power – logarithmic scale

Abstract

In this paper, within the framework of the С (N) D - formulation of the recovery problem, the problem
of optimal recovery of functions from anisotropic Sobolev classes in a power-logarithmic scale in the metric Lq
(2 ≤ q ≤
∞) is solved. Namely, in the case when the values l
(1)
N (f), ..., l(N)
N (f) of linear functionals l
(1)
N , ..., l(N)
N defined on the
considered functional class are used as numerical information about a function, firstly, the exact order of the recovery
error is established, and secondly, a specific computing unit ϕ¯N

¯l
(1)
N (f), ..., ¯l
(N)
N (f); ·

is indicated that implements the
established exact order.