Approximative characteristics of classes of functions $S_{p,\theta }^{\Omega }B({\mathbb{R}}^d)$ with a given majorant of mixed modulus of smoothness

Abstract

We obtain order estimates of approximation of functions from the classes $S_{p,\theta }^{\Omega }B({\mathbb{R}}^d)$ in the space $L_q({\mathbb{R}}^d)$, $1<p<q<\infty$, by entire functions of exponential type with supports of their Fourier transforms in sets generated by the level surfaces of a function $\Omega$.

arXiv comment15 pages, in Russian