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

Authors

  • 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

DOI:

Keywords:

Fourier sum, Weyl-Nagy class, asymptotic equality

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 $L_p, 1\le p\le\infty$.

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Published

2019-12-25

Issue

Vol. 25 No. 4 (2019)

Section

Articles

How to Cite

Serdyuk, A. S., and I. V. Sokolenko. “Approximation by Fourier Sums in Classes of Differentiable Functions With High Exponents of Smoothness”. Methods of Functional Analysis and Topology, vol. 25, no. 4, Dec. 2019, pp. 381-7, https://zen.imath.kiev.ua/index.php/mfat/article/view/740.