Approximative characteristics of the Nikol’skii – Besov classes of functions $S_{1, θ}^r B(\mathbb{R}^d)$

Abstract

UDC 517.51
We establish the exact-order estimates for the approximation of the classes $S^{\boldsymbol{r}}_{1,\theta}B \left(\mathbb{R}^d\right)$ by entire functions of exponential type with supports of their Fourier transforms lying in a step hyperbolic cross. The error of approximation is estimated in the metric of the Lebesgue space $L_q\left(\mathbb{R}^d\right),\; 1 < q \leq \infty.$