2017
Том 69
№ 9

All Issues

Entropy numbers and the widths of the classes $B_{p,θ}^r$ of periodic functions of many variables

Romanyuk A. S.


Abstract

We establish the exact order estimates for the entropy numbers of the Nikol’skii – Besov classes of periodic functions of two variables in the space $L_\infty$ and use the obtained results in estimating the lower bounds for Kolmogorov, linear, and trigonometric widths. We also study the behavior of similar approximating characteristics of the classes $B_{p,θ}^r$ of periodic functions of many variables in the spaces $L_1$ and $B_{1,1}$.

Citation Example: Romanyuk A. S. Entropy numbers and the widths of the classes $B_{p,θ}^r$ of periodic functions of many variables // Ukr. Mat. Zh. - 2016. - 68, № 10. - pp. 1403-1417.