论文标题
关于von Neumann的Ergodic定理的光谱措施和收敛速率
On spectral measures and convergence rates in von Neumann's Ergodic Theorem
论文作者
论文摘要
我们表明，冯·诺伊曼（Von Neumann）的Ergodic定理中的幂律衰减指数（对于离散系统）是频谱量值的频谱度量指数〜$ 1 $。在这项工作中，我们还证明，在没有光谱差距的情况下，在弱收敛的假设下，冯·诺伊曼（Von Neumann）的ergodic定理中时间平均水平的收敛速率取决于无限度的时间序列。
We show that the power-law decay exponents in von Neumann's Ergodic Theorem (for discrete systems) are the pointwise scaling exponents of a spectral measure at the spectral value~$1$. In this work we also prove that, under an assumption of weak convergence, in the absence of a spectral gap, the convergence rates of the time-average in von Neumann's Ergodic Theorem depend on sequences of time going to infinity.
