Estimates of approximation characteristics and properties of operators of the best approximation for the classes of periodic functions in the space $B_{1,1}$

Keywords: Nikol'skii-Besov classes, Sobolev classes, orthoprojection widths, best approximation

Abstract

UDC 517.51

We obtain the exact-order estimates for orthoprojection widths and similar approximation characteristics of the Sobolev classes $W^{\boldsymbol{r}}_{p,\boldsymbol{\alpha}}$ and Nikol'skii–Besov classes $B^{\boldsymbol{r}}_{p,\theta}$ of periodic functions of one and several variables in the norm of the space $B_{1,1}$.
In addition, we establish that the sequence of norms of linear operators that realize the orders of the best approximation of the classes $B^{\boldsymbol{r}}_{1,\theta}$ in space $B_{1,1}$ using trigonometric polynomials with ``numbers'' of harmonics from step hyperbolic crosses is unbounded in the multidimensional case.

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Published
18.08.2021
How to Cite
Romanyuk, A. S., and S. Y. Yanchenko. “Estimates of Approximation Characteristics and Properties of Operators of the Best Approximation for the Classes of Periodic Functions in the Space $B_{1,1}$”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, no. 8, Aug. 2021, pp. 1102 -19, doi:10.37863/umzh.v73i8.6755.
Section
Research articles