Matematicheskie Zametki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Matematicheskie Zametki, 2010, Volume 87, Issue 5, Pages 756–763
DOI: https://doi.org/10.4213/mzm8718 (Mi mzm8718) 		 
This article is cited in 9 scientific papers (total in 9 papers)

On the Constants in the Estimates of the Rate of Convergence in von Neumann's Ergodic Theorem

A. G. Kachurovskiia, V. V. Sedalishchevb

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Novosibirsk State University
Full-text PDF (410 kB) Citations (9)
References:
PDF
HTML
DOI: https://doi.org/10.4213/mzm8718
Abstract: We study the rate of convergence in von Neumann's ergodic theorem. We obtain constants connecting the power rate of convergence of ergodic means and the power singularity at zero of the spectral measure of the corresponding dynamical system (these concepts are equivalent to each other). All the results of the paper have obvious exact analogs for wide-sense stationary stochastic processes.
Keywords: von Neumann's ergodic theorem, ergodic mean, spectral measure, dynamical system, wide-sense stationary stochastic process, correlation coefficient, Darboux sum.
Received: 19.08.2009
English version:
Mathematical Notes, 2010, Volume 87, Issue 5, Pages 720–727
DOI: https://doi.org/10.1134/S000143461005010X
Bibliographic databases:
Document Type: Article
UDC: 517.987+519.214
Language: Russian
Citation: A. G. Kachurovskii, V. V. Sedalishchev, “On the Constants in the Estimates of the Rate of Convergence in von Neumann's Ergodic Theorem”, Mat. Zametki, 87:5 (2010), 756–763; Math. Notes, 87:5 (2010), 720–727
Citation in format AMSBIB
\Bibitem{KacSed10}
\by A.~G.~Kachurovskii, V.~V.~Sedalishchev
\paper On the Constants in the Estimates of the Rate of Convergence in von~Neumann's Ergodic Theorem
\jour Mat. Zametki
\yr 2010
\vol 87
\issue 5
\pages 756--763
\mathnet{http://mi.mathnet.ru/mzm8718}
\crossref{https://doi.org/10.4213/mzm8718}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2766588}
\elib{https://elibrary.ru/item.asp?id=15316090}
\transl
\jour Math. Notes
\yr 2010
\vol 87
\issue 5
\pages 720--727
\crossref{https://doi.org/10.1134/S000143461005010X}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000279600700010}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77954406935}
Linking options:
  • https://www.mathnet.ru/eng/mzm8718
  • https://doi.org/10.4213/mzm8718
  • https://www.mathnet.ru/eng/mzm/v87/i5/p756
    • This publication is cited in the following 9 articles:
    1. Moacir Aloisio, Silas L. Carvalho, César R. de Oliveira, Edson Souza, “On spectral measures and convergence rates in von Neumann's Ergodic theorem”, Monatsh Math, 203:3 (2024), 543  crossref
    2. A. G. Kachurovskii, I. V. Podvigin, A. J. Khakimbaev, “Uniform Convergence on Subspaces in von Neumann Ergodic Theorem with Discrete Time”, Math. Notes, 113:5 (2023), 680–693  mathnet  crossref  crossref  mathscinet
    3. A. G. Kachurovskii, I. V. Podvigin, V. E. Todikov, “Uniform convergence on subspaces in von Neumann's ergodic theorem with continuous time”, Sib. elektron. matem. izv., 20:1 (2023), 183–206  mathnet  crossref
    4. Ben-Artzi J., Morisse B., “Uniform Convergence in Von Neumann'S Ergodic Theorem in the Absence of a Spectral Gap”, Ergod. Theory Dyn. Syst., 41:6 (2021), PII S0143385720000309, 1601–1611  crossref  mathscinet  isi
    5. A. G. Kachurovskii, M. N. Lapshtaev, A. Zh. Khakimbaev, “Ergodicheskaya teorema fon Neimana i summy Feiera zaryadov na okruzhnosti”, Sib. elektron. matem. izv., 17 (2020), 1313–1321  mathnet  crossref
    6. A. G. Kachurovskii, I. V. Podvigin, “Estimates of the rate of convergence in the von Neumann and Birkhoff ergodic theorems”, Trans. Moscow Math. Soc., 77 (2016), 1–53  mathnet  crossref  elib
    7. A. G. Kachurovskii, V. V. Sedalishchev, “Constants in estimates for the rates of convergence in von Neumann's and Birkhoff's ergodic theorems”, Sb. Math., 202:8 (2011), 1105–1125  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    8. N. A. Dzhulaǐ, A. G. Kachurovskiǐ, “Constants in the estimates of the rate of convergence in von Neumann's ergodic theorem with continuous time”, Siberian Math. J., 52:5 (2011), 824–835  mathnet  crossref  mathscinet  isi
    9. Kachurovskii A.G., Sedalischev V.V., “Neravenstva, pozvolyayuschie otsenivat skorosti skhodimosti v ergodicheskikh teoremakh”, Vestnik Kemerovskogo gosudarstvennogo universiteta, 2011, no. 3-1, 250–254  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
    Statistics & downloads:
    Abstract page:688
    Full-text PDF :335
    References:88
    First page:25
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025