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Ukrainian Mathematical Journal

, Volume 64, Issue 5, pp 797–815 | Cite as

Approximation by interpolation trigonometric polynomials on classes of periodic analytic functions

  • A. S. Serdyuk
Article

We establish asymptotically unimprovable interpolation analogs of Lebesgue-type inequalities on the sets \( C_{\beta}^{\psi }{L_p} \) of (ψ, β)-differentiable functions generated by sequences ψ(k) that satisfy the d’Alembert conditions. We find asymptotic equalities for the least upper bounds of approximations by interpolation trigonometric polynomials on the classes \( C_{{\beta, p}}^{\psi } \), 1 ≤ p ≤ ∞.

Keywords

English Translation Trigonometric Polynomial Ukrainian National Academy Poisson Kernel Asymptotic Equality 
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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • A. S. Serdyuk
    • 1
  1. 1.KyivUkraine

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