On the rate of convergence in von Neumann's ergodic theorem with continuous time
Journal Article
·
· Sbornik. Mathematics
- S.L. Sobolev Institute for Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk (Russian Federation)
- Novosibirsk State University, Novosibirsk (Russian Federation)
The rate of convergence in von Neumann's mean ergodic theorem is studied for continuous time. The condition that the rate of convergence of the ergodic averages be of power-law type is shown to be equivalent to requiring that the spectral measure of the corresponding dynamical system have a power-type singularity at 0. This forces the estimates for the convergence rate in the above ergodic theorem to be necessarily spectral. All the results obtained have obvious exact analogues for wide-sense stationary processes. Bibliography: 7 titles.
- OSTI ID:
- 21418092
- Journal Information:
- Sbornik. Mathematics, Journal Name: Sbornik. Mathematics Journal Issue: 4 Vol. 201; ISSN 1064-5616
- Country of Publication:
- United States
- Language:
- English
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