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

### Abstract

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

Key words: Fourier sum, Weyl-Nagy class, asymptotic equality.

### Article Information

 Title Approximation by Fourier sums in classes of differentiable functions with high exponents of smoothness Source Methods Funct. Anal. Topology, Vol. 25 (2019), no. 4, 381-387 Milestones Received 21/05/2019 Copyright The Author(s) 2019 (CC BY-SA)

### Authors Information

A. S. Serdyuk
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs’ka str., Kyiv, 01601, Ukraine

I. V. Sokolenko
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs’ka str., Kyiv, 01601, Ukraine

### Citation Example

A. S. Serdyuk and I. V. Sokolenko, Approximation by Fourier sums in classes of differentiable functions with high exponents of smoothness, Methods Funct. Anal. Topology 25 (2019), no. 4, 381-387.

### BibTex

@article {MFAT1245,
AUTHOR = {A. S. Serdyuk and I. V. Sokolenko},
TITLE = {Approximation by Fourier sums in classes of differentiable functions with high exponents of smoothness},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {25},
YEAR = {2019},
NUMBER = {4},
PAGES = {381-387},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=1245},
}

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