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

  • A. S. Romanyuk

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 $B_{1,1}$.
Published
25.10.2016
How to Cite
RomanyukA. S. “Entropy Numbers and the Widths of the Classes $B_{p,θ}^r$ of Periodic functions of Many Variables”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 68, no. 10, Oct. 2016, pp. 1403-17, http://umj.imath.kiev.ua/index.php/umj/article/view/1928.
Section
Research articles