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Approximation of infinitely differentiable periodic functions by interpolation trigonometric polynomials

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Ukrainian Mathematical Journal Aims and scope

Abstract

We establish asymptotically unimprovable interpolation analogs of Lebesgue-type inequalities on the classes of periodic infinitely differentiable functions C βΨ 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 β,∞Ψ and C βΨ H ω.

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kyiv

    A. S. Serdyuk

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  1. A. S. Serdyuk
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 4, pp. 495–505, April, 2004.

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Serdyuk, A.S. Approximation of infinitely differentiable periodic functions by interpolation trigonometric polynomials. Ukr Math J 56, 601–613 (2004). https://doi.org/10.1007/s11253-005-0006-0

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  • DOI: https://doi.org/10.1007/s11253-005-0006-0

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