Characterization of Translation Bounded Measure Dynamical Systems and Positive Measure Dynamical Systems within the Spatial Processes

2025/08/24 by Sieron, Franziska
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.17425

Abstract

In this paper we consider spatial processes and measure dynamical systems over locally compact Abelian groups. We characterize when a spatial processes is equivalent to a translation bounded measure dynamical systems and we characterize when a spatial processes is equivalent to a positive measure dynamical systems. The basic idea of our approach is the identification of the elements of a spatial process with translation bounded measures respectively positive measures by applying the Gelfand theory of C^*-algebras.

Citations

• Stationary processes with pure point diffraction
• Stationary processes and pure point diffraction
• Dynamical systems on translation bounded measures: pure point dynamical and diffraction spectra
• Quasicrystals and almost periodicity
• Diffraction and Palm measure of point processes
• Metallic Phase with Long-Range Orientational Order and No Translational Symmetry
• Geometric Models for Quasicrystals I. Delone Sets of Finite Type

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