A spectral criterion for power-law convergence rate in the ergodic theorem for Zd and Rd actions Full article
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Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260 |
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| Output data | Year: 2024, Volume: 65, Number: 1, Pages: 76–95 Pages count : 20 DOI: 10.1134/S0037446624010099 | ||||||
| Tags | convergence rates in ergodic theorems, symmetric polynomial | ||||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0004 |
Abstract:
We prove the equivalence of the power-law convergence rate in the L2-norm of ergodic averages for Zd and Rd actions and the same power-law estimate for the spectral measure of symmetric d-dimensional parallelepipeds: for the degrees that are roots of some special symmetric polynomial in d variables. Particularly, all possible range of power-law rates is covered for d = 1.
Cite:
Kachurovskii A.G.
, Podvigin I.V.
, Todikov V.E.
, Khakimbaev A.Z.
A spectral criterion for power-law convergence rate in the ergodic theorem for Zd and Rd actions
Siberian Mathematical Journal. 2024. V.65. N1. P.76–95. DOI: 10.1134/S0037446624010099 WOS Scopus РИНЦ РИНЦ OpenAlex
A spectral criterion for power-law convergence rate in the ergodic theorem for Zd and Rd actions
Siberian Mathematical Journal. 2024. V.65. N1. P.76–95. DOI: 10.1134/S0037446624010099 WOS Scopus РИНЦ РИНЦ OpenAlex
Original:
Качуровский А.Г.
, Подвигин И.В.
, Тодиков В.Э.
, Хакимбаев А.Ж.
Спектральный критерий степенной скорости сходимости в эргодической теореме для Zd и Rd действий
Сибирский математический журнал. 2024. Т.65. №1. С.92–114. DOI: 10.33048/smzh.2024.65.109 РИНЦ
Спектральный критерий степенной скорости сходимости в эргодической теореме для Zd и Rd действий
Сибирский математический журнал. 2024. Т.65. №1. С.92–114. DOI: 10.33048/smzh.2024.65.109 РИНЦ
Dates:
| Submitted: | Jun 28, 2023 |
| Accepted: | Sep 25, 2023 |
| Published print: | Feb 7, 2024 |
| Published online: | Feb 7, 2024 |
Identifiers:
| Web of science: | WOS:001158248700017 |
| Scopus: | 2-s2.0-85188348709 |
| Elibrary: | 65969201 | 67311552 |
| OpenAlex: | W4391604077 |