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Approximation by Interpolation Trigonometric Polynomials in Metrics of the Space Lp on the Classes of Periodic Entire Functions*

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Ukrainian Mathematical Journal Aims and scope

A Correction to this article was published on 12 November 2019

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We establish asymptotic equalities for the least upper bounds of approximations by interpolation trigonometric polynomials with equidistant distribution of interpolation nodes \( {x}_k^{\left(n-1\right)}=\frac{2 k\pi}{2n-1},\kern0.33em k\in \mathbb{Z}, \) in metrics of the spaces Lp on the classes of 2⇡ -periodic functions that can be represented in the form of convolutions of functions 𝜑, 𝜑 ⊥ 1, from the unit ball in the space L1 with fixed generating kernels in the case where the modules of their Fourier coefficients ψ(k) satisfy the condition limk → ∞ψ(k + 1)/ψ(k) = 0. Similar estimates are also obtained for the classes of r –differentiable functions \( {W}_1^r \) with rapidly increasing exponents of smoothness r(r/n → ∞, n → ∞).

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  • 12 November 2019

    The title of the article should read:

    Approximation by Interpolation Trigonometric Polynomials in Metrics of the Space <Emphasis Type="Italic">L</Emphasis><Subscript><Emphasis Type="Italic">p</Emphasis></Subscript> on the Classes of Periodic Entire Functions

    The original article has been corrected.

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Authors and Affiliations

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

    A. S. Serdyuk & I. V. Sokolenko

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  1. A. S. Serdyuk
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  2. I. V. Sokolenko
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Correspondence to I. V. Sokolenko.

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The original version of this article was revised: The title of the article should read: Approximation by Interpolation Trigonometric Polynomials in Metrics of the Space Lp on the Classes of Periodic Entire Functions.

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, No. 2, pp. 283–292, February, 2019.

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Serdyuk, A.S., Sokolenko, I.V. Approximation by Interpolation Trigonometric Polynomials in Metrics of the Space Lp on the Classes of Periodic Entire Functions*. Ukr Math J 71, 322–332 (2019). https://doi.org/10.1007/s11253-019-01647-2

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  • DOI: https://doi.org/10.1007/s11253-019-01647-2

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