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Criterion for Exact Power Asymptotics in von Neumann’s Ergodic Theorem Full article

Journal Mathematical Notes
ISSN: 0001-4346 , E-ISSN: 1573-8876
Output data Year: 2026, Volume: 119, Number: 5-6, Pages: 911-918 Pages count : 8 DOI: 10.1134/s0001434626602741
Tags convergence rate in ergodic theorem, spectral measure, distribution.
Authors Elovatskii S.S. 1 , Podvigin I.V. 2
Affiliations
1 Novosibirsk State University, Novosibirsk, 630090, Russia
2 Sobolev Institute of Mathematics, Siberian Branch of Russian Academy of Sciences, Novosibirsk, 630090, Russia

Funding (1)

1 Министерство науки и высшего образования РФ FWNF-2026-0022

Abstract: Aspectral criterion for the exact power-law asymptotics of the norms of deviations from the limit of ergodic means in the von Neumann theorem is obtained for all possible exponents. This result strengthens and generalizes Ibragimov–Linnik’s theorem on asymptotics of these norms in the case of the existence of a spectral measure density continuous at the origin.
Cite: Elovatskii S.S. , Podvigin I.V.
Criterion for Exact Power Asymptotics in von Neumann’s Ergodic Theorem
Mathematical Notes. 2026. V.119. N5-6. P.911-918. DOI: 10.1134/s0001434626602741 WOS Scopus РИНЦ OpenAlex
Original: Еловацкий C.C. , Подвигин И.В.
Критерий точной степенной асимптотики в эргодической теореме фон Неймана
Математические заметки. 2026. Т.119. №5. С.699-708. DOI: 10.4213/mzm14854 OpenAlex
Dates:
Submitted: Sep 17, 2025
Accepted: Dec 15, 2025
Published print: Jul 26, 2026
Published online: Jul 26, 2026
Identifiers:
≡ Web of science: WOS:001831114400003
≡ Scopus: 2-s2.0-105045638170
≡ Elibrary: 91841343
≡ OpenAlex: W7171331933
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