Best approximations of the classes $B_{p,\,\theta}^{r}$ of periodic functions of many variables in uniform metric

  • A. S. Romanyuk

Abstract

We obtain estimates exact in order for the best approximations of the classes $B_{\infty,\,\theta}^{r}$ of periodic functions of two variables in the metric of $L_{\infty}$ by trigonometric polynomials whose spectrum belongs to a hyperbolic cross. We also investigate the best approximations of the classes $B_{p,\,\theta}^{r},\quad 1 \leq p < \infty$, of periodic functions of many variables in the metric of $L_{\infty}$ by trigonometric polynomials whose spectrum belongs to a graded hyperbolic cross.
Published
25.10.2006
How to Cite
Romanyuk, A. S. “Best Approximations of the Classes $B_{p,\,\theta}^{r}$ of Periodic Functions of Many Variables in Uniform Metric”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, no. 10, Oct. 2006, pp. 1395–1406, https://umj.imath.kiev.ua/index.php/umj/article/view/3541.
Section
Research articles