A note on the dynamics of linear automorphisms of a measure convolution algebra
Alexandre Baraviera, Elismar R. Oliveira, Fagner B. Rodrigues · arXiv (Cornell University) · 2013
In this work we are going to study the dynamics of the linear automorphisms of a measure convolution algebra over a finite group, $T(μ)=ν* μ$. 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 $\{ν^{n}\}_{n\in\mathbb{N}}$, where $G$ is a finite group, $ν\in\mathcal{P}(G)$ and $ν^n=\underbrace{ν\ast...\astν}_n$, trough the subgroup generated by his support.