On the constants in the estimates of the rate of convergence in von Neumann's ergodic theorem

被引：7
|
作者：
Kachurovskii, A. G. [1 ]
Sedalishchev, V. V. [2 ]
机构：
[1] Russian Acad Sci, Sobolev Inst Math, Novosibirsk 630090, Russia
[2] Novosibirsk State Univ, Novosibirsk 630090, Russia
来源：
MATHEMATICAL NOTES | 2010年 / 87卷 / 5-6期
关键词：
von Neumann's ergodic theorem; ergodic mean; spectral measure; dynamical system; wide-sense stationary stochastic process; correlation coefficient; Darboux sum;
D O I：
10.1134/S000143461005010X
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the rate of convergence in von Neumann's ergodic theorem. We obtain constants connecting the power rate of convergence of ergodic means and the power singularity at zero of the spectral measure of the corresponding dynamical system (these concepts are equivalent to each other). All the results of the paper have obvious exact analogs for wide-sense stationary stochastic processes.
引用
收藏
页码：720 / 727
页数：8
相关论文
共 50 条
  • [21] A detailed proof of the von Neumann’s Quantum Ergodic Theorem
    Lopes A.O.
    Sebastiani M.
    Quantum Studies: Mathematics and Foundations, 2017, 4 (3) : 263 - 285
  • [22] Normal typicality and von Neumann's quantum ergodic theorem
    Goldstein, Sheldon
    Lebowitz, Joel L.
    Mastrodonato, Christian
    Tumulka, Roderich
    Zanghi, Nino
    PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2010, 466 (2123): : 3203 - 3224
  • [23] ON THE POWER RATE OF CONVERGENCE IN WIENER'S ERGODIC THEOREM
    Podvigin, I., V
    ST PETERSBURG MATHEMATICAL JOURNAL, 2025,
  • [24] ERGODIC TYPE THEOREM FOR VON-NEUMANN ALGEBRAS
    ABDALLA, SM
    SZUCS, J
    ACTA SCIENTIARUM MATHEMATICARUM, 1974, 36 (1-2): : 167 - 172
  • [25] On individual subsequential ergodic theorem in von Neumann algebras
    Litvinov, S
    Mukhamedov, F
    STUDIA MATHEMATICA, 2001, 145 (01) : 55 - 62
  • [26] On the convergence rate in the uniform ergodic theorem
    Yoshimoto, T
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1996, 200 (01) : 149 - 161
  • [27] VON NEUMANN'S ERGODIC THEOREM AND FEJER SUMS FOR SIGNED MEASURES ON THE CIRCLE
    Kachurovskii, A. G.
    Lapshtaev, M. N.
    Khakimbaev, A. J.
    SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA, 2020, 17 : 1313 - 1321
  • [28] Interrelation between the convergence rates in von Neumann's and Birkhoff's ergodic theorems
    Sedalishchev, V. V.
    SIBERIAN MATHEMATICAL JOURNAL, 2014, 55 (02) : 336 - 348
  • [29] Interrelation between the convergence rates in von Neumann’s and Birkhoff’s ergodic theorems
    V. V. Sedalishchev
    Siberian Mathematical Journal, 2014, 55 : 336 - 348
  • [30] The Maximum Pointwise Rate of Convergence in Birkhoff’s Ergodic Theorem
    Kachurovskii A.G.
    Podvigin I.V.
    Svishchev A.A.
    Journal of Mathematical Sciences, 2021, 255 (2) : 119 - 123
12345