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

K.V. Pozharska; A.S. Romanyuk

doi:10.15421/242425

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

K.V. Pozharska (Institute of Mathematics of NAS of Ukraine, Chemnitz University of Technology), https://orcid.org/0000-0001-7599-8117
A.S. Romanyuk (Institute of Mathematics of NAS of Ukraine), https://orcid.org/0000-0002-6268-0799

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 $$$1\leqslant p \leqslant \infty$$$.

Keywords

Nikol'skii-Besov classes; Sobolev classes; best m-term trigonometric approximation

MSC 2020

42A10

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