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MAXIMUM RATE OF NORM CONVERGENCE IN THE ERGODIC THEOREM FOR GROUPS ℤd AND ℝd. / Kachurovskii, A. G.; Podvigin, I. V.; Khakimbaev, A. J.

в: Siberian Electronic Mathematical Reports, Том 22, № 1, 2025, стр. 67-83.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Kachurovskii, AG, Podvigin, IV & Khakimbaev, AJ 2025, 'MAXIMUM RATE OF NORM CONVERGENCE IN THE ERGODIC THEOREM FOR GROUPS ℤd AND ℝd', Siberian Electronic Mathematical Reports, Том. 22, № 1, стр. 67-83. https://doi.org/10.33048/semi.2025.22.006

APA

Kachurovskii, A. G., Podvigin, I. V., & Khakimbaev, A. J. (2025). MAXIMUM RATE OF NORM CONVERGENCE IN THE ERGODIC THEOREM FOR GROUPS ℤd AND ℝd. Siberian Electronic Mathematical Reports, 22(1), 67-83. https://doi.org/10.33048/semi.2025.22.006

Vancouver

Kachurovskii AG, Podvigin IV, Khakimbaev AJ. MAXIMUM RATE OF NORM CONVERGENCE IN THE ERGODIC THEOREM FOR GROUPS ℤd AND ℝd. Siberian Electronic Mathematical Reports. 2025;22(1):67-83. doi: 10.33048/semi.2025.22.006

Author

Kachurovskii, A. G. ; Podvigin, I. V. ; Khakimbaev, A. J. / MAXIMUM RATE OF NORM CONVERGENCE IN THE ERGODIC THEOREM FOR GROUPS ℤd AND ℝd. в: Siberian Electronic Mathematical Reports. 2025 ; Том 22, № 1. стр. 67-83.

BibTeX

@article{4375b94d80294e8aa10bab8df2c11ceb,
title = "MAXIMUM RATE OF NORM CONVERGENCE IN THE ERGODIC THEOREM FOR GROUPS ℤd AND ℝd",
abstract = "For d pairwise commuting automorphisms (flows) of a probability space, ergodic averages over parallelepipeds are considered. It is shown that the maximum rate of their convergence in the Lp-norm is (Formula presented.). A spectral criterion is also obtained for the maximum convergence rate in the L2-norm.",
keywords = "bundle of hyperplanes, coboundaries, rates of convergence in ergodic theorems, spectral measure",
author = "Kachurovskii, {A. G.} and Podvigin, {I. V.} and Khakimbaev, {A. J.}",
year = "2025",
doi = "10.33048/semi.2025.22.006",
language = "English",
volume = "22",
pages = "67--83",
journal = "Сибирские электронные математические известия",
issn = "1813-3304",
publisher = "Sobolev Institute of Mathematics",
number = "1",

}

RIS

TY - JOUR

T1 - MAXIMUM RATE OF NORM CONVERGENCE IN THE ERGODIC THEOREM FOR GROUPS ℤd AND ℝd

AU - Kachurovskii, A. G.

AU - Podvigin, I. V.

AU - Khakimbaev, A. J.

PY - 2025

Y1 - 2025

N2 - For d pairwise commuting automorphisms (flows) of a probability space, ergodic averages over parallelepipeds are considered. It is shown that the maximum rate of their convergence in the Lp-norm is (Formula presented.). A spectral criterion is also obtained for the maximum convergence rate in the L2-norm.

AB - For d pairwise commuting automorphisms (flows) of a probability space, ergodic averages over parallelepipeds are considered. It is shown that the maximum rate of their convergence in the Lp-norm is (Formula presented.). A spectral criterion is also obtained for the maximum convergence rate in the L2-norm.

KW - bundle of hyperplanes

KW - coboundaries

KW - rates of convergence in ergodic theorems

KW - spectral measure

UR - https://www.mendeley.com/catalogue/1e0ab4c1-54d0-3107-b21c-05561575b41d/

UR - https://math-semr.ru/sites/math-semr.ru/files/2025-03/p0067-0083.pdf

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-105001415009&origin=inward&txGid=79898c6da8101363f7d0251dafe801d7

U2 - 10.33048/semi.2025.22.006

DO - 10.33048/semi.2025.22.006

M3 - Article

VL - 22

SP - 67

EP - 83

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

IS - 1

ER -

ID: 65168505