The Lamperti correspondence extended to Lévy processes and semi-stable Markov processes in locally compact groups

We establish Lamperti representations for semi-stable Markov processes in locally compact groups. We also study the particular cases of processes with values in R$\mathbb{R}$ and C$\mathbb{C}$ under the hypothesis that they do not visit 0. These Lamperti representations yield some properties of these semi-stable Markov processes.