Maximum rate of norm convergence in the ergodic theorem for groups Z^d and R^d Full article
| Journal |
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports)
, E-ISSN: 1813-3304 |
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| Output data | Year: 2025, Volume: 22, Number: 1, Pages: 67-83 Pages count : 17 DOI: 10.33048/semi.2025.22.006 | ||||
| Tags | rates of convergence in ergodic theorems, spectral measure, coboundaries, bundle of hyperplanes | ||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0004 |
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 O( 1/t_1t_2···t_d). A spectral criterion is also obtained for the maximum convergence rate in the L2-norm.
Cite:
Kachurovskii A.G.
, Podvigin I.V.
, Khakimbaev A.J.
Maximum rate of norm convergence in the ergodic theorem for groups Z^d and R^d
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2025. V.22. N1. P.67-83. DOI: 10.33048/semi.2025.22.006 WOS Scopus
Maximum rate of norm convergence in the ergodic theorem for groups Z^d and R^d
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2025. V.22. N1. P.67-83. DOI: 10.33048/semi.2025.22.006 WOS Scopus
Dates:
| Submitted: | Aug 5, 2024 |
| Published print: | Mar 3, 2025 |
| Published online: | Mar 3, 2025 |
Identifiers:
| Web of science: | WOS:001473623500006 |
| Scopus: | 2-s2.0-105001415009 |
Citing:
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