Pure point spectrum for dynamical systems and mean almost periodicity

2020/06/18 by Daniel Lenz, Timo Spindeler, Lenz, Daniel +3 · 1 citation
Mathematics · #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Mathematical Dynamics and Fractals #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2006.10825

openalex publication_date 2020/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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