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Asymptotic Estimates for the Best Uniform Approximations of Classes of Convolution of Periodic Functions of High Smoothness

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Abstract

We find two-sided estimates for the best uniform approximations of classes of convolutions of 2𝜋-periodic functions from a unit ball of the space Lp,1 ≤ p < ∞; with fixed kernels such that the moduli of their Fourier coefficients satisfy the condition \( \sum \limits_{k=n+1}^{\infty}\psi (k)<\psi (n) \): In the case of \( \sum \limits_{k=n+1}^{\infty}\psi (k)=o(1)\psi (n) \); the obtained estimates become the asymptotic equalities.

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Authors and Affiliations

  1. Institute of Mathematics of the NAS of Ukraine, Kiev, Ukraine

    Anatolii S. Serdyuk & Igor V. Sokolenko

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  1. Anatolii S. Serdyuk
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  2. Igor V. Sokolenko
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Correspondence to Anatolii S. Serdyuk.

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Dedicated to the memory of Professor S.B. Stechkin and Professor S.A. Telyakovskii

Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 17, No. 3, pp. 396–413 July–September, 2020.

This work was partially supported by the Grant H2020-MSCA-RISE-2019, project number 873071 (SOMPATY: Spectral Optimization: From Mathematics to Physics and Advanced Technology).

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Serdyuk, A.S., Sokolenko, I.V. Asymptotic Estimates for the Best Uniform Approximations of Classes of Convolution of Periodic Functions of High Smoothness. J Math Sci 252, 526–540 (2021). https://doi.org/10.1007/s10958-020-05178-1

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