Pure point spectrum for dynamical systems and mean almost periodicity

Author
Lenz, Daniel
Spindeler, Timo
Strungaru, Nicolae
Faculty Advisor
Date
2020
Keywords
pure point spectrum , aperiodic order
Abstract (summary)
We consider metrizable ergodic topological dynamical systems over locally compact, σ-compact abelian groups. We study pure point spectrum via suitable notions of almost periodicity for the points of the dynamical system. More specifically, we characterize pure point spectrum via mean almost periodicity of generic points. We then go on and show how Besicovitch almost periodic points determine both eigenfunctions and the measure in this case. After this, we characterize those systems arising from Weyl almost periodic points and use this to characterize weak and Bohr almost periodic systems. Finally, we consider applications to aperiodic order.
Publication Information
Lenz, D., Spindeler, T., & Strungaru, N. (2020). Pure point spectrum for dynamical systems and mean almost periodicity. arXiv:2006.10825v1. https://arxiv.org/abs/2006.10825
DOI
Notes
Item Type
Report
Language
English
Rights
All Rights Reserved