On spectral measures and convergence rates in von Neumann's Ergodic Theorem

Autor:	Aloisio, M., Carvalho, S. L., de Oliveira, C. R., Souza, E.
Rok vydání:	2022
Předmět:	Mathematics - Spectral Theory Mathematics - Dynamical Systems
Druh dokumentu:	Working Paper
Popis:	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. Comment: Major changes following suggestions of the referee
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2209.05290 Zobrazit plný text záznamu View this record from Arxiv