RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Sibirsk. Mat. Zh.:
Year:
Volume:
Issue:
Page:
Find






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


Sibirsk. Mat. Zh., 2014, Volume 55, Number 2, Pages 412–426 (Mi smj2543)  

This article is cited in 3 scientific papers (total in 3 papers)

Interrelation between the convergence rates in von Neumann's and Birkhoff's ergodic theorems

V. V. Sedalishchev

Novosibirsk State University, Novosibirsk, Russia

Abstract: In the $L_p$ spaces, $1<p<\infty$, we prove some inequalities for discrete and continuous times that make it possible to obtain the convergence rate in Birkhoff's theorem in the presence of bounds on the convergence rate in von Neumann's ergodic theorem belonging to a sufficiently large rate range. The exact operator analogs of these inequalities for contraction semigroups in $L_p$ are given. These results also have the obvious exact analogs in the class of wide-sense stationary stochastic processes.

Keywords: von Neumann's ergodic theorem, Birkhoff's ergodic theorem, convergence rate of ergodic averages, wide-sense stationary stochastic process, contraction semigroups in $L_p$.

Full text: PDF file (354 kB)
References: PDF file   HTML file

English version:
Siberian Mathematical Journal, 2014, 55:2, 336–348

Bibliographic databases:

UDC: 517.987+519.214
Received: 14.06.2013

Citation: V. V. Sedalishchev, “Interrelation between the convergence rates in von Neumann's and Birkhoff's ergodic theorems”, Sibirsk. Mat. Zh., 55:2 (2014), 412–426; Siberian Math. J., 55:2 (2014), 336–348

Citation in format AMSBIB
\Bibitem{Sed14}
\by V.~V.~Sedalishchev
\paper Interrelation between the convergence rates in von Neumann's and Birkhoff's ergodic theorems
\jour Sibirsk. Mat. Zh.
\yr 2014
\vol 55
\issue 2
\pages 412--426
\mathnet{http://mi.mathnet.ru/smj2543}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3237344}
\transl
\jour Siberian Math. J.
\yr 2014
\vol 55
\issue 2
\pages 336--348
\crossref{https://doi.org/10.1134/S0037446614020165}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000335167300016}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84899687263}


Linking options:
  • http://mi.mathnet.ru/eng/smj2543
  • http://mi.mathnet.ru/eng/smj/v55/i2/p412

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. I. V. Podvigin, “On the rate of convergence in the individual ergodic theorem for the action of a semigroup”, Siberian Adv. Math., 26:2 (2016), 139–151  mathnet  crossref  crossref  mathscinet  elib
    2. 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
    3. I. V. Podvigin, “Estimates for correlation in dynamical systems: from Hölder continuous functions to general observables”, Siberian Adv. Math., 28:3 (2018), 187–206  mathnet  crossref  crossref  elib
  • Сибирский математический журнал Siberian Mathematical Journal
    Number of views:
    This page:440
    Full text:108
    References:37
    First page:12

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020