论文摘要
In this paper, we develop semi-classical analysis on H-type groups. We define semi-classical pseudodifferential operators, prove the boundedness of their action on square integrable functions and develop a symbolic calculus. Then, we define the semi-classical measures of bounded families of square integrable functions which consist of a pair formed by a measure defined on the product of the group and its unitary dual, and by a field of trace class positive operators acting on the Hilbert spaces of the representations. We illustrate the theory by analyzing examples, which show in particular that this semi-classical analysis takes into account the finite-dimensional representations of the group, even though they are negligible with respect to the Plancherel measure.
论文目录
文章来源
类型: 期刊论文
作者: Clotilde Fermanian Kammerer,Véronique Fischer
来源: Science China(Mathematics) 2019年06期
年度: 2019
分类: 基础科学
专业: 数学
单位: Université Paris-Est, Laboratoire d’Analyse et de Mathématiques Appliquées (UMR 8050),Department of Mathematical Sciences, University of Bath
分类号: O152
页码: 1057-1086
总页数: 30
文件大小: 361K
下载量: 12