%0 Journal Article
%T Ergodic properties of pseudo-differential operators on compact Lie groups
%J International Journal of Nonlinear Analysis and Applications
%I Semnan University
%Z 2008-6822
%A Faghih, Zahra
%A Ghaemi, Mohammad Bagher
%D 2022
%\ 07/01/2022
%V 13
%N 2
%P 1703-1711
%! Ergodic properties of pseudo-differential operators on compact Lie groups
%K Pseudo-differential operators
%K Lamperti operator
%K Dominated Ergodic Estimate
%K trigonometrically well-bounded
%K M. Riesz theorem
%K Adjoints
%R 10.22075/ijnaa.2022.25780.3126
%X Let $ \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.
%U https://ijnaa.semnan.ac.ir/article_6317_44701cf03a8b35ab3ad12c7b96378d8c.pdf