On the speed of convergence in the ergodic theorem for shift operators
Abstract Given a probability space $(X,\mu )$ , a square integrable function f on such space and a (unilateral or bilateral) shift operator T , we prove under suitable assumptions that the ergodic means $N^{-1}\sum _{n=0}^{N-1} T^nf$ converge pointwise almost everywhere to zero with a speed of convergence which, up to a small logarithmic transgression, is essentially of the order of $N^{-1/2}$ . We also provide a few applications of our results, especially in the case of shifts associated with toral endomorphisms.
Authors
- Nikolaos Chalmoukis (ORCID: https://orcid.org/0000-0001-5210-8206)
- Bianca Gariboldi (ORCID: https://orcid.org/0000-0001-8714-4135)
- Leonardo Colzani
- Alessandro Monguzzi (ORCID: https://orcid.org/0000-0003-3233-5000)
Institutions
- University of Bergamo (IT)
- University of Milano-Bicocca (IT)
Publication Details
- Journal
- Canadian Journal of Mathematics
- Published
- 2024-11-04
- DOI
- https://doi.org/10.4153/s0008414x24000658
- Citations
- 1
- Primary Topic
- advanced mathematical theories
- Type
- article
- Field-Weighted Citation Impact
- 0.89
Funders
- Istituto Nazionale di Alta Matematica "Francesco Severi"
- European Commission
- Hellenic Foundation for Research and Innovation