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arXiv · 1305.4374

Estimates of the uniform approximations by Zygmund sums on the classes of convolutions of periodic functions

A. S. Serdyuk·U. Z. Grabova
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Abstract

We obtain order-exact estimates for uniform approximations by using Zygmund sums $Z^{s}_{n}$ of classes $C^{\psi}_{\beta,p}$ of $2\pi$-periodic continuous functions $f$ representable by convolutions of functions from unit balls of the space $L_{p}$, $1< p<\infty$, with a fixed kernels $\Psi_{\beta}\in L_{p'}$, $\frac{1}{p}+\frac{1}{p'}=1$. In addition, we find a set of allowed values of parameters (that define the class $C^{\psi}_{\beta,p}$ and the linear method $Z^{s}_{n}$) for which Zygmund sums and Fejer sums realize the order of the best uniform approximations by trigonometric polynomials of those classes.

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BibTeXRIS

A. S. Serdyuk, U. Z. Grabova. 2013-05-19. Estimates of the uniform approximations by Zygmund sums on the classes of convolutions of periodic functions. https://arxiv.org/abs/1305.4374

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