2018
Том 70
№ 2

# Kolmogorov widths and bilinear approximations of the classes of periodic functions of one and many variables

Romanyuk A. S.

Abstract

We obtain the exact order estimates for the Kolmogorov widths of the classes $W^g_p$ of periodic functions of one variable generated by the integral operators with kernels $g(x, y)$ from the Nikol’skii – Besov classes $B^r_{p,\theta}$. We also study the behavior of bilinear approximations to the classes $W^r_{p,\alpha}$ of periodic multivariate functions with bounded mixed derivative in the spaces $L_{q_1,q_2}$ for some relations between the parameters $r_1, p, q_1, q_2$.

Citation Example: Romanyuk A. S. Kolmogorov widths and bilinear approximations of the classes of periodic functions of one and many variables // Ukr. Mat. Zh. - 2018. - 70, № 2. - pp. 224-235.