Ergodic properties of pseudo-differential operators on compact Lie groups

Document Type : Research Paper

Authors

School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran

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

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Volume 13, Issue 2
July 2022
Pages 1703-1711
  • Receive Date: 02 January 2022
  • Accept Date: 13 March 2022