2018
Том 70
№ 5

# Trigonometric and linear widths for the classes of periodic multivariable functions

Romanyuk A. S.

Abstract

We establish the exact-order estimates for the trigonometric widths of Nikol’skii – Besov $B^r_{\infty ,\theta}$ and Sobolev $W^r_{\infty, \alpha}$ classes of periodic multivariable functions in the space $L_q,\; 1 < q < \infty$. The behavior of the linear widths of Nikol’skii – Besov $B^r_{\infty ,\theta}$ classes in the space $L_q$ is investigated for certain relations between the parameters $p$ and $q$.

Citation Example: Romanyuk A. S. Trigonometric and linear widths for the classes of periodic multivariable functions // Ukr. Mat. Zh. - 2017. - 69, № 5. - pp. 670-681.