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Ukrainian Mathematical Journal

, Volume 60, Issue 7, pp 1144–1152 | Cite as

Approximation of Poisson integrals by one linear approximation method in uniform and integral metrics

  • A. S. Serdyuk
Article

We obtain asymptotic equalities for the least upper bounds of approximations of classes of Poisson integrals of periodic functions by a linear approximation method of special form in the metrics of the spaces C and L p .

Keywords

Periodic Function Approximation Theory Linear Method Trigonometric Polynomial Sharp Estimate 
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References

  1. 1.
    A. S. Serdyuk, “On one linear method for approximation of periodic functions,” in: Problems of the Theory of Approximation of Functions and Related Problems [in Ukrainian], Vol. 1, No. 1, Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv (2004), pp. 295–336.Google Scholar
  2. 2.
    A. I. Stepanets, Classification and Approximation of Periodic Functions [in Russian], Naukova Dumka, Kiev (1987).zbMATHGoogle Scholar
  3. 3.
    A. I. Stepanets, Methods of Approximation Theory [in Russian], Vol. 1, Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv (2002).Google Scholar
  4. 4.
    A. S. Serdyuk, “Approximation of classes of analytic functions by Fourier series in the uniform metric,” Ukr. Mat. Zh., 57, No. 8, 1079–1096 (2005).zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    N. P. Korneichuk, Exact Constants in Approximation Theory [in Russian], Nauka, Moscow (1987).Google Scholar
  6. 6.
    A. S. Serdyuk, “Approximation of classes of analytic functions by Fourier sums in the metric of the space L p,” Ukr. Mat. Zh., 57, No. 10, 1395–1408 (2005).zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  • A. S. Serdyuk
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKyivUkraine

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