On the speed of convergence in the ergodic theorem for shift operators
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866913580707741696 |
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| author | Chalmoukis, Nikolaos Colzani, Leonardo Gariboldi, Bianca Monguzzi, Alessandro |
| author_facet | Chalmoukis, Nikolaos Colzani, Leonardo Gariboldi, Bianca Monguzzi, Alessandro |
| contents | Given a probability space $(X,μ)$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_08922 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the speed of convergence in the ergodic theorem for shift operators Chalmoukis, Nikolaos Colzani, Leonardo Gariboldi, Bianca Monguzzi, Alessandro Classical Analysis and ODEs Dynamical Systems Functional Analysis 47A35, 37A30 Given a probability space $(X,μ)$, 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. |
| title | On the speed of convergence in the ergodic theorem for shift operators |
| topic | Classical Analysis and ODEs Dynamical Systems Functional Analysis 47A35, 37A30 |
| url | https://arxiv.org/abs/2312.08922 |