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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2023, Volume 20, Issue 1, Pages 183–206
DOI: https://doi.org/10.33048/semi.2023.20.016
(Mi semr1580)
 

This article is cited in 4 scientific papers (total in 4 papers)

Real, complex and functional analysis

Uniform convergence on subspaces in von Neumann's ergodic theorem with continuous time

A. G. Kachurovskiia, I. V. Podvigina, V. E. Todikovab

a Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
b Novosibirsk State Technical University, pr. K. Marksa, 20 630073, Novosibirsk, Russia
Full-text PDF (471 kB) Citations (4)
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Abstract: Power-law uniform (in the operator norm) convergence on vector subspaces with their own norms in von Neumann's ergodic theorem with continuous time is considered. All possible exponents of the considered power-law convergence are found; for each of these exponents, spectral criteria for such convergence are given and a complete description of all such subspaces is obtained. Uniform convergence over the entire space takes place only in trivial cases, which explains the interest in the uniform convergence just on subspaces.
In addition, along the way, the old convergence rate estimates in the von Neumann ergodic theorem for (semi)flows are generalized and refined.
Keywords: von Neumann's ergodic theorem, rates of convergence in ergodic theorems, power-law uniform convergence.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0004
The work was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project FWNF-2022-0004).
Received July 3, 2022, published March 1, 2023
Document Type: Article
UDC: 517.987+519.214
Language: English
Citation: A. G. Kachurovskii, I. V. Podvigin, V. E. Todikov, “Uniform convergence on subspaces in von Neumann's ergodic theorem with continuous time”, Sib. Èlektron. Mat. Izv., 20:1 (2023), 183–206
Citation in format AMSBIB
\Bibitem{KacPodTod23}
\by A.~G.~Kachurovskii, I.~V.~Podvigin, V.~E.~Todikov
\paper Uniform convergence on subspaces in von Neumann's ergodic theorem with continuous time
\jour Sib. \`Elektron. Mat. Izv.
\yr 2023
\vol 20
\issue 1
\pages 183--206
\mathnet{http://mi.mathnet.ru/semr1580}
\crossref{https://doi.org/10.33048/semi.2023.20.016}
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  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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