A Zero-One Law for the Rates of Convergence in the Birkhoff Ergodic Theorem with Continuous Time | Sciact - Система учета научной деятельности ИМ СО РАН

A Zero-One Law for the Rates of Convergence in the Birkhoff Ergodic Theorem with Continuous Time Научная публикация

Журнал

Siberian Advances in Mathematics
ISSN: 1055-1344 , E-ISSN: 1934-8126

Вых. Данные

Год: 2022, Том: 32, Номер: 3, Страницы: 186-196 Страниц : 11 DOI: 10.1134/s1055134422030026

Ключевые слова

Birkhoff ergodic theorem; lattice of estimates; natural extension of an endomorphism; optimal estimates; rates of convergence in ergodic theorems

Авторы

Kachurovskii A.G. ¹ , Podvigin I.V. ^1,2 , Svishchev A.A. ²

Организации

1	Sobolev Institute of Mathematics
2	Novosibirsk State University

Информация о финансировании (1)

Институт математики им. С.Л. Соболева СО РАН

0314-2019-0005

We consider monotone pointwise estimates for the rates of convergence in the Birkhoff ergodic theorem with continuous time. For an ergodic semiflow in a Lebesgue space, we prove that such estimates hold either on a null measure set or on a full measure set. It is shown that monotone estimates that hold almost everywhere always exist. We study the lattice of such estimates and also consider some questions concerning their unimprovability.

Kachurovskii A.G. , Podvigin I.V. , Svishchev A.A.
A Zero-One Law for the Rates of Convergence in the Birkhoff Ergodic Theorem with Continuous Time
Siberian Advances in Mathematics. 2022. V.32. N3. P.186-196. DOI: 10.1134/s1055134422030026 Scopus РИНЦ OpenAlex

Качуровский А.Г. , Подвигин И.В. , Свищёв A.A.
Закон нуля или единицы в эргодической теореме Биркгофа с непрерывным временем
Математические труды. 2021. Т.24. №2. С.65-80. DOI: 10.33048/mattrudy.2021.24.205 РИНЦ MathNet OpenAlex

Опубликована online:

2 сент. 2022 г.

Scopus:	2-s2.0-85137813083
РИНЦ:	51300991
OpenAlex:	W4294335362

БД	Цитирований
Scopus	3
OpenAlex	1
РИНЦ	1