Order estimates of approximation characteristics of functions from anisotropic Nikol'skii-Besov classes

TL;DR

This paper provides precise order estimates for how well functions from anisotropic Nikol'skii-Besov classes can be approximated by Fourier sections, with errors measured in the supremum norm.

Contribution

It presents exact order estimates for approximation errors of functions in anisotropic Nikol'skii-Besov classes using Fourier sections, advancing understanding of their approximation properties.

Findings

Derived exact order estimates of approximation errors

Quantified deviations in the $L_{ty}$ metric

Enhanced theoretical understanding of anisotropic Besov class approximations

Abstract

We obtained exact order estimates of the deviation of functions from anisotropic Nikol'skii-Besov classes $B^{\boldsymbol{r}}_{p,\theta}(\mathbb{R}^d)$ from their sections of the Fourier integral. The error of the approximation is estimated in the metric of Lebesgue space $L_{\infty}(\mathbb{R}^d)$.