Estimation of the Entropy Numbers and Kolmogorov Widths for the Nikol’skii–Besov Classes of Periodic Functions of Many Variables

  • A. S. Romanyuk

Abstract

We establish order estimates for the entropy numbers of the Nikol’skii–Besov classes $B_{p,θ}^r$ of periodic functions of many variables in the space $L_q$ with certain relations between the parameters $p$ and $q$. By using the obtained lower estimates of the entropy numbers, we establish the exact-order estimates for the Kolmogorov widths of the same classes of functions in the space $L_1$.
Published
25.11.2015
How to Cite
RomanyukA. S. “Estimation of the Entropy Numbers and Kolmogorov Widths for the Nikol’skii–Besov Classes of Periodic Functions of Many Variables”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, no. 11, Nov. 2015, pp. 1540-56, http://umj.imath.kiev.ua/index.php/umj/article/view/2088.
Section
Research articles