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arXiv · 1906.02531

Approximation by Fourier sums in classes of differentiable functions with high exponents of smoothness

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

We find asymptotic equalities for the exact upper bounds of approximations by Fourier sums of Weyl-Nagy classes $W^r_{β,p}, 1\le p\le\infty,$ for rapidly growing exponents of smoothness $r$ $(r/n\rightarrow\infty)$ in the uniform metric. We obtain similar estimates for approximations of the classes $W^r_{β,1}$ in metrics of the spaces $L_p, 1\le p\le\infty$.

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A. S. Serdyuk, I. V. Sokolenko. 2019-06-06. Approximation by Fourier sums in classes of differentiable functions with high exponents of smoothness. https://arxiv.org/abs/1906.02531

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