Geodesic
Exponent of Convergence of a Sequence of Ergodic Averages
Matematičeskie zametki, Tome 112 (2022) no. 2, pp. 251-262

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For a sequence of ergodic averages, we consider its exponent of convergence, which is a numerical characteristic of two-sided power-law estimates of the rate of pointwise convergence of this sequence. Criteria for the boundary values 1 and $\infty$ of the exponent of convergence are given. Functions cohomologous to zero with a given the exponent of convergence are also described.
Keywords: Birkhoff's ergodic theorem, rates of convergence in ergodic theorems, the exponent of convergence, Tanny–Woś spaces. 
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     author = {I. V. Podvigin},
     title = {Exponent of {Convergence} of a {Sequence} of {Ergodic} {Averages}},
     journal = {Matemati\v{c}eskie zametki},
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     publisher = {mathdoc},
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     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2022_112_2_a7/}
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I. V. Podvigin. Exponent of Convergence of a Sequence of Ergodic Averages. Matematičeskie zametki, Tome 112 (2022) no. 2, pp. 251-262. http://geodesic.mathdoc.fr/item/MZM_2022_112_2_a7/