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.

Full Text

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
MathSciNet	MR4049692
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},
  MRNUMBER = {MR4049692},
       URL = {http://mfat.imath.kiev.ua/article/?id=1245},
}

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