The best $m$-term trigonometric approximations of the classes of periodic functions of one and many variables in the space $B_{q,1}$

TL;DR

This paper derives exact order estimates for the best $m$-term trigonometric approximations of Nikol'skii-Besov and Sobolev classes of periodic functions in the space $B_{q,1}$, covering both univariate and multivariate cases.

Contribution

It provides new precise order estimates for $m$-term trigonometric approximations of specific function classes in the space $B_{q,1}$, including univariate and multivariate cases.

Findings

Exact order estimates for approximation characteristics in $B_{q,1}$.

Order of approximation for classes $B^r_{p, heta}$ and $W^r_{p, {oldsymbol{eta}}}$.

Results applicable to both one-variable and many-variable periodic functions.

Abstract

Exact order estimates are obtained of the best $m$-term trigonometric approximations of the Nikol'skii-Besov classes $B^r_{p, \theta}$ of periodic functions of one and many variables in the space $B_{q,1}$. In the univariate case ($d=1$), we get the orders of the respective approximation characteristics on the classes $B^r_{p, \theta}$ as well as on the Sobolev classes $W^r_{p, {\boldsymbol{\alpha}}}$ in the space $B_{\infty,1}$ in the case $1\leq p \leq \infty$.