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Approximation by Fourier Sums in the Classes of Weyl–Nagy Differentiable Functions with High Exponent of Smoothness

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Ukrainian Mathematical Journal Aims and scope

We establish asymptotic estimates for the least upper bounds of approximations in the uniform metric by Fourier sums of order n − 1 in the classes of 2𝜋-periodic Weyl–Nagy differentiable functions \( {W}_{\beta, p}^r \), 1 ≤ p ≤ ∞, β ∈ ℝ, with high exponents of smoothness \( r\left(r-1\ge \sqrt{n}\right) \). We also establish similar estimates for the function classes \( {W}_{\beta, 1}^r \)in metrics of the spaces Lp, 1 ≤ p ≤ ∞.

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Authors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences of Ukraine, 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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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 5, pp. 685–700, May, 2022. Ukrainian DOI: https://doi.org/10.37863/umzh.v74i5.7136.

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Serdyuk, A.S., Sokolenko, I.V. Approximation by Fourier Sums in the Classes of Weyl–Nagy Differentiable Functions with High Exponent of Smoothness. Ukr Math J 74, 783–800 (2022). https://doi.org/10.1007/s11253-022-02101-6

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  • DOI: https://doi.org/10.1007/s11253-022-02101-6

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