2017
Том 69
№ 9

All Issues

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

Romanyuk A. S.


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 $L_1$.

English version (Springer): Ukrainian Mathematical Journal 67 (2015), no. 11, pp 1739-1757.

Citation Example: Romanyuk A. S. Estimation of the Entropy Numbers and Kolmogorov Widths for the Nikol’skii–Besov Classes of Periodic Functions of Many Variables // Ukr. Mat. Zh. - 2015. - 67, № 11. - pp. 1540-1556.