Abstract
In this paper, we study an algebra $\mathcal{A}$ consisting of all arithmetic functions, and corresponding dynamical systems acting on $% \mathcal{A}$ determined by a fixed prime $p$. Starting from free probabilistic models on $\mathcal{A}$ determined by $p$, we construct certain group dynamical systems induced by the additive group $\Bbb{R}$ of all real numbers. We investigate the basic properties and free-probabilistic data of such dynamical systems by constructing corresponding crossed product algebras.
Citation
Ilwoo Cho. "Dynamical systems on arithmetic functions determined by primes." Banach J. Math. Anal. 9 (1) 173 - 215, 2015. https://doi.org/10.15352/bjma/09-1-15
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