On spectral measures and convergence rates in von Neumann’s Ergodic theorem

Monatshefte für Mathematik Pub Date : 2024-01-22 DOI:10.1007/s00605-023-01928-w

引用次数: 0

Abstract

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.

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论冯-诺依曼遍历定理中的谱量和收敛率

摘要我们证明了 von Neumann Ergodic Theorem（针对离散系统）中的幂律衰减指数是光谱量在光谱值为 1 时的点式缩放指数。在这项工作中，我们还证明了在弱收敛的假设下，在没有谱差距的情况下，von Neumann Ergodic Theorem 中的时间平均值的收敛率取决于无穷大的时间序列。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Monatshefte für Mathematik

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