Affiliation:
1. Institute of Mathematics of the NAS of Ukraine, Kyiv, Ukraine
Abstract
We have obtained the exact-order estimates for some approximative characteristics of the Sobolev classes $\mathbb{W}^{\boldsymbol{r}}_{p,\boldsymbol{\alpha}}$ and Nikоl'skii--Besov classes $\mathbb{B}^{\boldsymbol{r}}_{p,\theta}\ $ of periodic functions of one and several variables in the norm of the space $B_{\infty, 1}$. Properties of the linear operators realizing the orders of the best approximation for the classes $\mathbb{B}^{\boldsymbol{r}}_{\infty, \theta}$ in this space by trigonometric polynomials generated by a set of harmonics with $``$numbers$"$ from step hyperbolic crosses are investigated.
Publisher
Institute of Applied Mathematics and Mechanics of the National Academy of Sciences of Ukraine
Cited by
5 articles.
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