Ukrainian Mathematical Journal

, Volume 56, Issue 4, pp 601–613 | Cite as

Approximation of infinitely differentiable periodic functions by interpolation trigonometric polynomials

  • A. S. Serdyuk


We establish asymptotically unimprovable interpolation analogs of Lebesgue-type inequalities on the classes of periodic infinitely differentiable functions C Ψ β C whose elements can be represented in the form of convolutions with fixed generating kernels. We obtain asymptotic equalities for upper bounds of approximations by interpolation trigonometric polynomials on the classes C Ψ β,∞ and C Ψ β Hω.


Periodic Function Differentiable Function Trigonometric Polynomial Fixed Generate Asymptotic Equality 
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Copyright information

© Springer Science+Business Media, Inc. 2004

Authors and Affiliations

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

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