2017
Том 69
№ 5

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

Romanyuk A. S.

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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.

English version (Springer): Ukrainian Mathematical Journal 58 (2006), no. 10, pp 1582-1596.

Citation Example: Romanyuk A. S. Best approximations of the classes $B_{p,\,\theta}^{r}$ of periodic functions of many variables in uniform metric // Ukr. Mat. Zh. - 2006. - 58, № 10. - pp. 1395–1406.

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