Standard

Uniform Convergence on Subspaces in the von Neumann Ergodic Theorem with Discrete Time. / Kachurovskii, A. G.; Podvigin, I. V.; Khakimbaev, A. Zh.

In: Mathematical Notes, Vol. 113, No. 5-6, 06.2023, p. 680-693.

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

Harvard

Kachurovskii, AG, Podvigin, IV & Khakimbaev, AZ 2023, 'Uniform Convergence on Subspaces in the von Neumann Ergodic Theorem with Discrete Time', Mathematical Notes, vol. 113, no. 5-6, pp. 680-693. https://doi.org/10.1134/S0001434623050073

APA

Kachurovskii, A. G., Podvigin, I. V., & Khakimbaev, A. Z. (2023). Uniform Convergence on Subspaces in the von Neumann Ergodic Theorem with Discrete Time. Mathematical Notes, 113(5-6), 680-693. https://doi.org/10.1134/S0001434623050073

Vancouver

Kachurovskii AG, Podvigin IV, Khakimbaev AZ. Uniform Convergence on Subspaces in the von Neumann Ergodic Theorem with Discrete Time. Mathematical Notes. 2023 Jun;113(5-6):680-693. doi: 10.1134/S0001434623050073

Author

Kachurovskii, A. G. ; Podvigin, I. V. ; Khakimbaev, A. Zh. / Uniform Convergence on Subspaces in the von Neumann Ergodic Theorem with Discrete Time. In: Mathematical Notes. 2023 ; Vol. 113, No. 5-6. pp. 680-693.

BibTeX

@article{2be737f762e141e5a253277d179b273a,
title = "Uniform Convergence on Subspaces in the von Neumann Ergodic Theorem with Discrete Time",
abstract = "We consider the power-law uniform (in the operator norm) convergence on vector subspaces with their own norms in the von Neumann ergodic theorem with discrete time. All possible exponents of the considered power-law convergence are found; for each of these exponents, spectral criteria for such convergence are given and the complete description of all such subspaces is obtained. Uniform convergence on the whole space takes place only in the trivial cases, which explains the interest in uniform convergence precisely on subspaces. In addition, by the way, old estimates of the rates of convergence in the von Neumann ergodic theorem for measure-preserving mappings are generalized and refined.",
keywords = "power-law uniform convergence, rate of convergence in ergodic theorems, von Neumann ergodic theorem",
author = "Kachurovskii, {A. G.} and Podvigin, {I. V.} and Khakimbaev, {A. Zh}",
note = "This work was carried out in the framework of the state assignment at Institute of Mathematics, Siberian Branch of Russian Academy of Sciences (grant no. FWNF-2022-0004).",
year = "2023",
month = jun,
doi = "10.1134/S0001434623050073",
language = "English",
volume = "113",
pages = "680--693",
journal = "Mathematical Notes",
issn = "0001-4346",
publisher = "PLEIADES PUBLISHING INC",
number = "5-6",

}

RIS

TY - JOUR

T1 - Uniform Convergence on Subspaces in the von Neumann Ergodic Theorem with Discrete Time

AU - Kachurovskii, A. G.

AU - Podvigin, I. V.

AU - Khakimbaev, A. Zh

N1 - This work was carried out in the framework of the state assignment at Institute of Mathematics, Siberian Branch of Russian Academy of Sciences (grant no. FWNF-2022-0004).

PY - 2023/6

Y1 - 2023/6

N2 - We consider the power-law uniform (in the operator norm) convergence on vector subspaces with their own norms in the von Neumann ergodic theorem with discrete time. All possible exponents of the considered power-law convergence are found; for each of these exponents, spectral criteria for such convergence are given and the complete description of all such subspaces is obtained. Uniform convergence on the whole space takes place only in the trivial cases, which explains the interest in uniform convergence precisely on subspaces. In addition, by the way, old estimates of the rates of convergence in the von Neumann ergodic theorem for measure-preserving mappings are generalized and refined.

AB - We consider the power-law uniform (in the operator norm) convergence on vector subspaces with their own norms in the von Neumann ergodic theorem with discrete time. All possible exponents of the considered power-law convergence are found; for each of these exponents, spectral criteria for such convergence are given and the complete description of all such subspaces is obtained. Uniform convergence on the whole space takes place only in the trivial cases, which explains the interest in uniform convergence precisely on subspaces. In addition, by the way, old estimates of the rates of convergence in the von Neumann ergodic theorem for measure-preserving mappings are generalized and refined.

KW - power-law uniform convergence

KW - rate of convergence in ergodic theorems

KW - von Neumann ergodic theorem

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85163150206&origin=inward&txGid=298b3045692dfa144ff6c26330c17330

UR - https://www.mendeley.com/catalogue/6ab72504-25ca-3bd8-8281-8f85193797de/

U2 - 10.1134/S0001434623050073

DO - 10.1134/S0001434623050073

M3 - Article

VL - 113

SP - 680

EP - 693

JO - Mathematical Notes

JF - Mathematical Notes

SN - 0001-4346

IS - 5-6

ER -

ID: 55562306