On spectral measures and convergence rates in von Neumann's Ergodic Theorem
Spectral Theory
2023-12-13 v2 Dynamical Systems
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~. 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.
Keywords
Cite
@article{arxiv.2209.05290,
title = {On spectral measures and convergence rates in von Neumann's Ergodic Theorem},
author = {M. Aloisio and S. L. Carvalho and C. R. de Oliveira and E. Souza},
journal= {arXiv preprint arXiv:2209.05290},
year = {2023}
}
Comments
Major changes following suggestions of the referee