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Ukrainian Mathematical Journal

, Volume 59, Issue 8, pp 1224–1237 | Cite as

Asymptotics of the values of approximations in the mean for classes of differentiable functions by using biharmonic Poisson integrals

  • Yu. I. Kharkevych
  • I. V. Kal’chuk
Article

Abstract

We obtain complete asymptotic expansions for the exact upper bounds of the approximations of functions from the classes W 1 r , rN, and \(\overline W _1^r \), rN\{1}, by their biharmonic Poisson integrals.

Keywords

Differentiable Function Formal Series Trigonometric Series Ukrainian National Academy Poisson Kernel 
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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • Yu. I. Kharkevych
    • 1
  • I. V. Kal’chuk
    • 1
  1. 1.Volyn UniversityLuts’k

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