Order estimates of approximative characteristics of functions from classes $S^{r}_{1,\theta}B(\mathbb{R}^d)$

TL;DR

This paper derives precise order estimates for approximating certain function classes using entire functions with Fourier support in step hyperbolic crosses, measured in Lebesgue spaces.

Contribution

It provides exact order estimates for approximation errors of classes $S^{r}_{1, heta}B$ by entire functions with Fourier support in step hyperbolic crosses.

Findings

Exact order estimates of approximation errors obtained.

Results valid in Lebesgue spaces $L_q( ^d)$ for $1<q\leq\infty$.

Advances understanding of approximation properties of these function classes.

Abstract

We obtained exact order estimates of approximation of the classes $S^{\boldsymbol{r}}_{1,\theta}B$ by entire functions of exponential type with supports of their Fourier transforms in step hyperbolic cross. The error of the approximation estimated in the metric of Lebesgue spaces, $L_q(\mathbb{R}^d)$, $1<q\leqslant \infty$.