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Sibirskii Matematicheskii Zhurnal, 2022, Volume 63, Number 2, Pages 379–390
DOI: https://doi.org/10.33048/smzh.2022.63.209 (Mi smj7663) 		 
This article is cited in 4 scientific papers (total in 4 papers)

On possible estimates of the rate of pointwise convergence in the Birkhoff ergodic theorem

I. V. Podviginab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
Full-text PDF (371 kB) Citations (4)
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DOI: https://doi.org/10.33048/smzh.2022.63.209
Abstract: We study the separation from zero of a sequence $\phi$ to obtain the estimates of the form ${\phi(n)/n}$ for the rate of pointwise convergence of ergodic averages. Each of these $\phi$ is shown to be separated from zero for mixings which is not always so for weak mixings. Moreover, for the characteristic function of a nontrivial set, it is shown that there exists a measure preserving transformation with arbitrarily slow decay of ergodic averages.
Keywords: Birkhoff ergodic theorem, ergodic theorems for subsequences, rate of convergence in ergodic theorems.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 0314-2019-0005
The work was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project 0314–2019–0005).
Received: 07.06.2021
Revised: 07.06.2021
Accepted: 10.12.2021
English version:
Siberian Mathematical Journal, 2022, Volume 63, Issue 2, Pages 316–325
DOI: https://doi.org/10.1134/S0037446622020094
Document Type: Article
UDC: 517.987
Language: Russian
Citation: I. V. Podvigin, “On possible estimates of the rate of pointwise convergence in the Birkhoff ergodic theorem”, Sibirsk. Mat. Zh., 63:2 (2022), 379–390; Siberian Math. J., 63:2 (2022), 316–325
Citation in format AMSBIB
\Bibitem{Pod22}
\by I.~V.~Podvigin
\paper On possible estimates of the rate of pointwise convergence in the Birkhoff ergodic theorem
\jour Sibirsk. Mat. Zh.
\yr 2022
\vol 63
\issue 2
\pages 379--390
\mathnet{http://mi.mathnet.ru/smj7663}
\transl
\jour Siberian Math. J.
\yr 2022
\vol 63
\issue 2
\pages 316--325
\crossref{https://doi.org/10.1134/S0037446622020094}
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