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Asymptotics of Sums of Cosine Series with Fractional Monotonicity Coefficients

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Abstract

The paper examines the following question: Under what orders of monotonicity are the upper and lower bounds of the sum of a cosine series near zero valid if they are obtained using the function \(\sum_{n=0}^{[\pi/x]}(n+1)\Delta(\mathbf a)_n\)?

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References

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Funding

This work was supported by the Russian Science Foundation under grant 21-11-00131 at Lomonosov Moscow State University.

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, 119991, Russia

    M. I. D’yachenko

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

    M. I. D’yachenko

Authors
  1. M. I. D’yachenko
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Corresponding author

Correspondence to M. I. D’yachenko.

Additional information

Translated from Matematicheskie Zametki, 2021, Vol. 110, pp. 865–874 https://doi.org/10.4213/mzm13180.

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D’yachenko, M.I. Asymptotics of Sums of Cosine Series with Fractional Monotonicity Coefficients. Math Notes 110, 894–902 (2021). https://doi.org/10.1134/S0001434621110250

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  • DOI: https://doi.org/10.1134/S0001434621110250

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