Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-682213220220701Ergodic properties of pseudo-differential operators on compact Lie groups17031711631710.22075/ijnaa.2022.25780.3126ENZahra FaghihSchool of Mathematics, Iran University of Science and Technology, Narmak, Tehran, IranMohammad BagherGhaemiSchool of Mathematics, Iran University of Science and Technology, Narmak, Tehran, IranJournal Article20220102Let $ \mathbb{G} $ be a compact Lie group. This article shows that a contraction pseudo-differential operator $ A_{\tau} $ on $ L^{p}(\mathbb{G}) $ has a Dominated Ergodic Estimate (DEE), and is trigonometrically well-bounded. Then we express ergodic generalization of the Vector-Valued M. Riesz theorem for invertible contraction pseudo-differential operator $ A_{\tau} $ on $ L^{p}(\mathbb{G}) $. For this purpose, we show that $ A_{\tau} $ is a Lamperti operator. Then we find a formula for its symbols $ \tau$. According to this formula, a representation for the symbol of adjoint and products is given.https://ijnaa.semnan.ac.ir/article_6317_44701cf03a8b35ab3ad12c7b96378d8c.pdf