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arXiv · 2008.01450

Asymptotic estimates for the best uniform approximations of classes of convolution of periodic functions of high smoothness

A. S. Serdyuk·I. V. Sokolenko
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Abstract

We find two-sides estimates for the best uniform approximations of classes of convolutions of $2\pi$-periodic functions from unit ball of the space $L_p, 1 \le p <\infty,$ with fixed kernels, modules of Fourier coefficients of which satisfy the condition $\sum\limits_{k=n+1}^\infty\psi(k)<\psi(n).$ In the case of $\sum\limits_{k=n+1}^\infty\psi(k)=o(1)\psi(n)$ the obtained estimates become the asymptotic equalities.

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A. S. Serdyuk, I. V. Sokolenko. 2020-08-04. Asymptotic estimates for the best uniform approximations of classes of convolution of periodic functions of high smoothness. https://arxiv.org/abs/2008.01450

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