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

  • O. Ya. Radchenko
  • S. Ya. Yanchenko

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 $L_q\left(\mathbb{R}^d\right),\; 1 < q \leq \infty.$
Published
25.10.2019
How to Cite
RadchenkoO. Y., and YanchenkoS. Y. “Approximative Characteristics of the Nikol’skii – Besov classes of Functions $S_{1, θ}^r B(\mathbb{R}^d)$”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, no. 10, Oct. 2019, pp. 1405-21, http://umj.imath.kiev.ua/index.php/umj/article/view/1523.
Section
Research articles