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Journal of Mathematical Sciences

, Volume 143, Issue 3, pp 3039–3052 | Cite as

On approximating periodic functions by singular integrals with positive kernels

  • N. Yu. Dodonov
  • V. V. Zhuk
Article
  • 22 Downloads

Abstract

In the two-dimensional case, new approximation characteristics for functions belonging to saturation classes of continuity modules for the spaces Lp of periodic functions are obtained. The problem of approximating a function by an analog of Fejér’s integral in the space of periodic functions square integrable on the period is considered. Bibliography: 5 titles.

Keywords

Periodic Function Continuity Module Singular Integral Approximation Characteristic Positive Kernel 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    A. S. Zhuk and V. V. Zhuk, “On approximating periodic functions using linear approximation methods,” Zap. Nauchn. Semin. POMI, 337, 134–164 (2006).MathSciNetGoogle Scholar
  2. 2.
    V. V. Zhuk, Approximation of Periodic Functions [in Russian], Leningrad (1982).Google Scholar
  3. 3.
    V. V. Zhuk, Strong Approximation of Periodic Functions [in Russian], Leningrad (1989).Google Scholar
  4. 4.
    H. Bateman and A. Erdélyi, Tables of Integral Transforms [Russian translation], Vol. 1, Moscow (1969).Google Scholar
  5. 5.
    A. Zygmund, Trigonometrical Series [Russian translation], Vol. 1, Moscow (1965).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • N. Yu. Dodonov
    • 1
  • V. V. Zhuk
    • 1
  1. 1.St.Petersburg State UniversitySt.PetersburgRussia

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