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Uniform Approximations by Fourier Sums in Classes of Generalized Poisson Integrals

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Abstract

We find asymptotic equalities for the exact upper bounds of approximations by Fourier sums in the uniform metric in classes of 2π-periodic functions, representable in the form of convolutions of functions φ, which belong to the unit balls of the spaces Lp, with generalized Poisson kernels. For the asymptotic equalities obtained we introduce the estimates of the remainder, which are expressed in an explicit form via the parameters of the problem.

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Authors and Affiliations

  1. Institute of Mathematics of Ukrainian National Academy of Sciences, Tereshchenkivska st. 3, 01601, Kyiv-4, Ukraine

    A. S. Serdyuk

  2. Graz University of Technology, Kopernikusgasse 24/II, 8010, Graz, Austria

    T. A. Stepanyuk

Authors
  1. A. S. Serdyuk
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  2. T. A. Stepanyuk
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Corresponding author

Correspondence to T. A. Stepanyuk.

Additional information

The second author is supported by the Austrian Science Fund FWF project F5503 (part of the Special Research Program (SFB) “Quasi-Monte Carlo Methods: Theory and Applications”.

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Serdyuk, A.S., Stepanyuk, T.A. Uniform Approximations by Fourier Sums in Classes of Generalized Poisson Integrals. Anal Math 45, 201–236 (2019). https://doi.org/10.1007/s10476-018-0310-1

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  • DOI: https://doi.org/10.1007/s10476-018-0310-1

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