Standard

Criterion for Exact Power Asymptotics in von Neumann’s Ergodic Theorem. / Elovatskii, S. S.; Podvigin, I. V.

In: Mathematical Notes, Vol. 119, No. 5, 26.07.2026, p. 911-918.

Research output: Contribution to journal › Article › peer-review

Harvard

Elovatskii, SS & Podvigin, IV 2026, 'Criterion for Exact Power Asymptotics in von Neumann’s Ergodic Theorem', Mathematical Notes, vol. 119, no. 5, pp. 911-918. https://doi.org/10.1134/S0001434626602741

APA

Elovatskii, S. S., & Podvigin, I. V. (2026). Criterion for Exact Power Asymptotics in von Neumann’s Ergodic Theorem. Mathematical Notes, 119(5), 911-918. https://doi.org/10.1134/S0001434626602741

Vancouver

Elovatskii SS, Podvigin IV. Criterion for Exact Power Asymptotics in von Neumann’s Ergodic Theorem. Mathematical Notes. 2026 Jul 26;119(5):911-918. doi: 10.1134/S0001434626602741

Author

Elovatskii, S. S. ; Podvigin, I. V. / Criterion for Exact Power Asymptotics in von Neumann’s Ergodic Theorem. In: Mathematical Notes. 2026 ; Vol. 119, No. 5. pp. 911-918.

BibTeX

@article{08011d4a9a4d4722914f4d568bf1cb71,
title = "Criterion for Exact Power Asymptotics in von Neumann{\textquoteright}s Ergodic Theorem",
abstract = "A spectral 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{\textquoteright}s theorem on asymptotics of these norms in the case of the existence of a spectral measure density continuous at the origin.",
keywords = "convergence rate in ergodic theorem, distribution, spectral measure, скорость сходимости в эргодической теореме, спектральная мера, распределение",
author = "Elovatskii, {S. S.} and Podvigin, {I. V.}",
note = "Elovatskii, S.S., Podvigin, I.V. Criterion for Exact Power Asymptotics in von Neumann{\textquoteright}s Ergodic Theorem. Math Notes 119, 911–918 (2026). https://doi.org/10.1134/S0001434626602741 The work of the second author was carried out as part of the state order for the Sobolev Institute of Mathematics of Siberian Branch of Russian Academy of Sciences (grant no. FWNF-2026-0022).",
year = "2026",
month = jul,
day = "26",
doi = "10.1134/S0001434626602741",
language = "English",
volume = "119",
pages = "911--918",
journal = "Mathematical Notes",
issn = "0001-4346",
publisher = "Pleiades Publishing",
number = "5",

}

RIS

TY - JOUR

T1 - Criterion for Exact Power Asymptotics in von Neumann’s Ergodic Theorem

AU - Elovatskii, S. S.

AU - Podvigin, I. V.

N1 - Elovatskii, S.S., Podvigin, I.V. Criterion for Exact Power Asymptotics in von Neumann’s Ergodic Theorem. Math Notes 119, 911–918 (2026). https://doi.org/10.1134/S0001434626602741 The work of the second author was carried out as part of the state order for the Sobolev Institute of Mathematics of Siberian Branch of Russian Academy of Sciences (grant no. FWNF-2026-0022).

PY - 2026/7/26

Y1 - 2026/7/26

N2 - A spectral 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.

AB - A spectral 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.

KW - convergence rate in ergodic theorem

KW - distribution

KW - spectral measure

KW - скорость сходимости в эргодической теореме

KW - спектральная мера

KW - распределение

UR - https://www.mendeley.com/catalogue/fecc52d6-e014-36f5-b323-f58f1ea35b9b/

UR - https://www.scopus.com/pages/publications/105045638170

U2 - 10.1134/S0001434626602741

DO - 10.1134/S0001434626602741

M3 - Article

VL - 119

SP - 911

EP - 918

JO - Mathematical Notes

JF - Mathematical Notes

SN - 0001-4346

IS - 5

ER -

ID: 83072113