Convergence rates in the ergodic theorem for unitary actions of compactly generated abelian groups

Convergence rates in the ergodic theorem for unitary actions of compactly generated abelian groups Full article

Journal

Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260

Output data

Year: 2025, Volume: 66, Number: 3, Pages: 691-701 Pages count : 11 DOI: 10.1134/S0037446625030097

Funding (1)

Sobolev Institute of Mathematics

FWNF-2022-0004

For the convergence rates in the ergodic theorem for unitary actions of locally compact compactly generated abelian groups, we obtain a spectral criterion in terms of the singularity of the spectral measure in a neighborhood of the unit character. It is thus shown that estimates for these rates, as for the classical ergodic theorems for actions of the groups Z and R studied previously, are necessarily of spectral nature.

Kachurovskii A.G. , Podvigin I.V. , Todikov V.E.
Convergence rates in the ergodic theorem for unitary actions of compactly generated abelian groups
Siberian Mathematical Journal. 2025. V.66. N3. P.691-701. DOI: 10.1134/S0037446625030097 WOS Scopus РИНЦ OpenAlex

Качуровский А.Г. , Подвигин И.В. , Тодиков В.Э.
Скорости сходимости в эргодической теореме для унитарных действий абелевых групп компактного происхождения
Сибирский математический журнал. 2025. Т.66. №3. С.438-449. DOI: 10.33048/smzh.2025.66.309 РИНЦ MathNet

Submitted:	Dec 30, 2024
Accepted:	Apr 25, 2025
Published print:	Jun 2, 2025
Published online:	Jun 2, 2025

Web of science:	WOS:001500903100006
Scopus:	2-s2.0-105007091709
Elibrary:	82395835
OpenAlex:	W4410947146

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