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arXiv · 2508.17425

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

Franziska Sieron
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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.

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Franziska Sieron. 2025-08-24. Characterization of Translation Bounded Measure Dynamical Systems and Positive Measure Dynamical Systems within the Spatial Processes. https://arxiv.org/abs/2508.17425

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