A note on the dynamics of linear automorphisms of a measure convolution algebra

Abstract

In this work we are going to study the dynamics of the linear automorphisms of a measure convolution algebra over a finite group, $T(\mu )=\nu \ast \mu$. In order to understand an classify the asymptotic behavior of this dynamical system we provide an alternative to classical results, a very direct way to understand convergence of the sequence $\{{\nu }^n{\}}_{n\in \mathbb{N}}$, where $G$ is a finite group, $\nu \in \mathcal{P}(G)$ and ${\nu }^n=\underset{n}{\underbrace{\nu \ast ...\ast \nu }}$, trough the subgroup generated by his support.

14 pages