Pure Point spectrum for measure dynamical systems on locally compact Abelian groups
Mathematical Physics
2020-04-02 v2 math.MP
Abstract
We show equivalence of pure point diffraction and pure point dynamical spectrum for measurable dynamical systems build from locally finite measures on locally compact Abelian groups. This generalizes all earlier results of this type. Our approach is based on a study of almost periodicity in a Hilbert space. It allows us to set up a perturbation theory for arbitrary equivariant measurable perturbations.
Cite
@article{arxiv.0704.2498,
title = {Pure Point spectrum for measure dynamical systems on locally compact Abelian groups},
author = {Daniel Lenz and Nicolae Strungaru},
journal= {arXiv preprint arXiv:0704.2498},
year = {2020}
}