This article is cited in 3 scientific papers (total in 3 papers)
Interrelation between the convergence rates in von Neumann's and Birkhoff's ergodic theorems
V. V. Sedalishchev
Novosibirsk State University, Novosibirsk, Russia
In the $L_p$ spaces, $1<p<\infty$, we prove some inequalities for discrete and continuous times that make it possible to obtain the convergence rate in Birkhoff's theorem in the presence of bounds on the convergence rate in von Neumann's ergodic theorem belonging to a sufficiently large rate range. The exact operator analogs of these inequalities for contraction semigroups in $L_p$ are given. These results also have the obvious exact analogs in the class of wide-sense stationary stochastic processes.
von Neumann's ergodic theorem, Birkhoff's ergodic theorem, convergence rate of ergodic averages, wide-sense stationary stochastic process, contraction semigroups in $L_p$.
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Siberian Mathematical Journal, 2014, 55:2, 336–348
V. V. Sedalishchev, “Interrelation between the convergence rates in von Neumann's and Birkhoff's ergodic theorems”, Sibirsk. Mat. Zh., 55:2 (2014), 412–426; Siberian Math. J., 55:2 (2014), 336–348
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\paper Interrelation between the convergence rates in von Neumann's and Birkhoff's ergodic theorems
\jour Sibirsk. Mat. Zh.
\jour Siberian Math. J.
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A. G. Kachurovskii, I. V. Podvigin, “Estimates of the rate of convergence in the von Neumann and Birkhoff ergodic theorems”, Trans. Moscow Math. Soc., 77 (2016), 1–53
I. V. Podvigin, “Estimates for correlation in dynamical systems: from Hölder continuous functions to general observables”, Siberian Adv. Math., 28:3 (2018), 187–206
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