Approximation of Nikol'skii-Besov functional classes $S^r_{1,\theta}B(\mathbb{R}^d)$ by entire functions of a special form

Abstract

We establish the exact-order estimates for the approximation of functions from the Nikol'skii-Besov classes $S^{\boldsymbol{r}}_{1,\theta} B(\mathbb{R}^d)$, $d\geqslant 1$, by entire function exponential type with some restrictions for their spectrum. The error of the approximation is estimated in the metric of the Lebesgue space $L_{\infty}(\mathbb{R}^d)$.