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Deviations of Fejer Sums and Rates of Convergence in the von Neumann Ergodic Theorem

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Abstract

It turns out that the deviations of the Fejer sums for continuous 2π-periodic functions and the rates of convergence in the von Neumann ergodic theorem can both be calculated using, in fact, the same formulas (by integrating the Fejer kernels). As a result, for many dynamical systems popular in applications, the rates of convergence in the von Neumann ergodic theorem can be estimated with a sharp leading coefficient of the asymptotic by applying S.N. Bernstein’s more than hundred-year old results in harmonic analysis.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia

    A. G. Kachurovskii

  2. Novosibirsk State University, Novosibirsk, 630090, Russia

    K. I. Knizhov

Authors
  1. A. G. Kachurovskii
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  2. K. I. Knizhov
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Correspondence to A. G. Kachurovskii.

Additional information

Original Russian Text © A.G. Kachurovskii, K.I. Knizhov, 2018, published in Doklady Akademii Nauk, 2018, Vol. 480, No. 1, pp. 21–24.

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Kachurovskii, A.G., Knizhov, K.I. Deviations of Fejer Sums and Rates of Convergence in the von Neumann Ergodic Theorem. Dokl. Math. 97, 211–214 (2018). https://doi.org/10.1134/S1064562418030031

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