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Estimation of the Approximation of Continuous Periodic Functions by Fourier Sums

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Abstract

An asymptotically exact estimate for the norm of the difference between a function and the partial sum of its Fourier series is obtained in terms of the modulus of continuity of the function. The values of the modulus of continuity of the argument that are less than the optimal one are considered.

DOI 10.1134/S1061920823040179

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Authors and Affiliations

  1. Department of Mechanics and Mathematics, Moscow State University, Moscow, 119991, Russia

    T.Yu. Semenova

  2. Moscow Center for Fundamental and Applied Mathematics, Moscow, 119991, Russia

    T.Yu. Semenova

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  1. T.Yu. Semenova
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Correspondence to T.Yu. Semenova.

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Semenova, T. Estimation of the Approximation of Continuous Periodic Functions by Fourier Sums. Russ. J. Math. Phys. 30, 691–700 (2023). https://doi.org/10.1134/S1061920823040179

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  • DOI: https://doi.org/10.1134/S1061920823040179

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