Convergence rates in the ergodic theorem for unitary actions of compactly generated abelian groups Full article
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Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260 |
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| Output data | Year: 2025, Volume: 66, Number: 3, Pages: 691-701 Pages count : 11 DOI: 10.1134/S0037446625030097 | ||
| Tags | convergence rates in the ergodic theorem, compactly generated abelian groups | ||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0004 |
Abstract:
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.
Cite:
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
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
Original:
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
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
Dates:
| Submitted: | Dec 30, 2024 |
| Accepted: | Apr 25, 2025 |
| Published print: | Jun 2, 2025 |
| Published online: | Jun 2, 2025 |
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