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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 | ||
| تاریخ دریافت: 12 دی 1400، تاریخ پذیرش: 22 اسفند 1400 | ||
| 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 | ||
| مراجع | ||
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