A. G. Kachurovskii, I. V. Podvigin, A. A. Svishchev, “The maximum pointwise rate of convergence in Birkhoff's ergodic theorem”, Zap. Nauchn. Sem. POMI, 2020, Volume 498,Pages <nobr>18

This article is cited in 4 papers

I

The maximum pointwise rate of convergence in Birkhoff's ergodic theorem

A. G. Kachurovskii^a, I. V. Podvigin^ab, A. A. Svishchev^b

^a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
^b Novosibirsk State University

Abstract: A criterion for the maximum possible pointwise convergence rate in Birkhoff's ergodic theorem for ergodic semiflows in a Lebesgue space is obtained. It is proved that higher rates of convergence in this theorem are impossible.

Key words and phrases: ergodic semiflow, Birkhoff's ergodic theorem, rates of convergence.

UDC: 517.987, 519.216

Received: 31.03.2020