@article {
author = {Faghih, Zahra and Ghaemi, Mohammad},
title = {Ergodic properties of pseudo-differential operators on compact Lie groups},
journal = {International Journal of Nonlinear Analysis and Applications},
volume = {13},
number = {2},
pages = {1703-1711},
year = {2022},
publisher = {Semnan University},
issn = {2008-6822},
eissn = {2008-6822},
doi = {10.22075/ijnaa.2022.25780.3126},
abstract = {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.},
keywords = {Pseudo-differential operators,Lamperti operator,Dominated Ergodic Estimate,trigonometrically well-bounded,M. Riesz theorem,Adjoints},
url = {https://ijnaa.semnan.ac.ir/article_6317.html},
eprint = {https://ijnaa.semnan.ac.ir/article_6317_44701cf03a8b35ab3ad12c7b96378d8c.pdf}
}