English

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

Dynamical Systems 2025-08-26 v1

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 CC^*-algebras.

Keywords

Cite

@article{arxiv.2508.17425,
  title  = {Characterization of Translation Bounded Measure Dynamical Systems and Positive Measure Dynamical Systems within the Spatial Processes},
  author = {Franziska Sieron},
  journal= {arXiv preprint arXiv:2508.17425},
  year   = {2025}
}