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Uspekhi Mat. Nauk, 2020, Volume 75, Issue 3(453), Pages 3–36 (Mi umn9940)  

This article is cited in 1 scientific paper (total in 1 paper)

Non-uniform Kozlov–Treschev averagings in the ergodic theorem

V. I. Bogachevab

a Lomonosov Moscow State University
b National Research University Higher School of Economics

Abstract: Generalizations and refinements are given for results of Kozlov and Treschev on non-uniform averagings in the ergodic theorem in the case of operator semigroups on spaces of integrable functions and semigroups of measure-preserving transformations. Conditions on the averaging measures are studied under which the averages converge for broad classes of integrable functions.
Bibliography: 96 items.

Keywords: ergodic theorem, operator semigroup, averaging of a semigroup.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-31-20008
20-01-00432
Foundation for the Advancement of Theoretical Physics and Mathematics BASIS 18-1-6-83-1
Moscow Center of Fundamental and Applied Mathematics
This research was supported by the Russian Foundation for Basic Research (grants nos. 18-31-20008 and 20-01-00432), Moscow Center of Fundamental and Applied Mathematics, and the Foundation for the Advancement of Theoretical Physics and Mathematics BASIS (grant no. 18-1-6-83-1).


DOI: https://doi.org/10.4213/rm9940

Full text: PDF file (790 kB)
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English version:
Russian Mathematical Surveys, 2020, 75:3, 393–425

Bibliographic databases:

UDC: 517.5+519.2
MSC: Primary 37A30; Secondary 28D10
Received: 02.03.2020

Citation: V. I. Bogachev, “Non-uniform Kozlov–Treschev averagings in the ergodic theorem”, Uspekhi Mat. Nauk, 75:3(453) (2020), 3–36; Russian Math. Surveys, 75:3 (2020), 393–425

Citation in format AMSBIB
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\by V.~I.~Bogachev
\paper Non-uniform Kozlov--Treschev averagings in the ergodic theorem
\jour Uspekhi Mat. Nauk
\yr 2020
\vol 75
\issue 3(453)
\pages 3--36
\mathnet{http://mi.mathnet.ru/umn9940}
\crossref{https://doi.org/10.4213/rm9940}
\transl
\jour Russian Math. Surveys
\yr 2020
\vol 75
\issue 3
\pages 393--425
\crossref{https://doi.org/10.1070/RM9940}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85096318068}


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  • https://doi.org/10.4213/rm9940
  • http://mi.mathnet.ru/eng/umn/v75/i3/p3

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. I. Bogachev, “Approximations of Nonlinear Integral Functionals of Entropy Type”, Proc. Steklov Inst. Math., 310 (2020), 1–11  mathnet  crossref  crossref  isi
  • Успехи математических наук Russian Mathematical Surveys
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