Approximation of Nikol'skii-Besov functional classes $S_{1,\theta }^{r}B({\mathbb{R}}^d)$ 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 $S_{1,\theta }^{\mathbf{r}}B({\mathbb{R}}^d)$, $d⩾1$, 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 $L_{\infty }({\mathbb{R}}^d)$.

11 pages, in Ukrainian