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On spectral measures and convergence rates in von Neumann's Ergodic Theorem
- Publication Year :
- 2022
-
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.<br />Comment: Major changes following suggestions of the referee
- Subjects :
- Mathematics - Spectral Theory
Mathematics - Dynamical Systems
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2209.05290
- Document Type :
- Working Paper