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A spectral criterion for power-law convergence rate in the ergodic theorem for Zd and Rd actions Full article

Journal Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260
Output data Year: 2024, Volume: 65, Number: 1, Pages: 76–95 Pages count : DOI: 10.1134/S0037446624010099
Tags convergence rates in ergodic theorems, symmetric polynomial
Authors Kachurovskii A.G. 1 , Podvigin I.V. 1 , Todikov V.E. 1,2 , Khakimbaev A.Z. 3
Affiliations
1 Sobolev Institute of Mathematics
2 Novosibirsk State Technical University
3 Novosibirsk State University

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
Original: Качуровский А.Г. , Подвигин И.В. , Тодиков В.Э. , Хакимбаев А.Ж.у.
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
Citing: Пока нет цитирований
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