Deviations of Fejer Sums and Rates of Convergence in the von Neumann Ergodic Theorem
- Authors: Kachurovskii A.G.1, Knizhov K.I.2
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Affiliations:
- Sobolev Institute of Mathematics, Siberian Branch
- Novosibirsk State University
- Issue: Vol 97, No 3 (2018)
- Pages: 211-214
- Section: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/225496
- DOI: https://doi.org/10.1134/S1064562418030031
- ID: 225496
Cite item
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.
About the authors
A. G. Kachurovskii
Sobolev Institute of Mathematics, Siberian Branch
Author for correspondence.
Email: agk@math.nsc.ru
Russian Federation, Novosibirsk, 630090
K. I. Knizhov
Novosibirsk State University
Email: agk@math.nsc.ru
Russian Federation, Novosibirsk, 630090