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

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, $L_q(\mathbb{R}^d)$, $1<q\leqslant \infty$.