Ergodic properties of pseudo-differential operators on compact Lie groups

	Ergodic properties of pseudo-differential operators on compact Lie groups
International Journal of Nonlinear Analysis and Applications
مقاله 137، دوره 13، شماره 2، مهر 2022، صفحه 1703-1711 اصل مقاله (395.93 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.25780.3126
نویسندگان
Zahra Faghih؛ Mohammad Bagher Ghaemi^*
School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran
چکیده
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.
کلیدواژه‌ها
Pseudo-differential operators؛ Lamperti operator؛ Dominated Ergodic Estimate؛ trigonometrically well-bounded؛ M. Riesz theorem؛ Adjoints
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