论文标题
离散串联表示的密度定理限于晶格
The density theorem for discrete series representations restricted to lattices
论文作者
论文摘要
本文考虑了离散串联表示的晶格轨道的跨度属性与相关晶格共同体积之间的关系。重点放在密度定理上，该密度定理提供了表征循环向量和分离向量以及框架和riesz序列的三分法切开术。我们提供了密度定理的基本说明，该论述仅基于谐波分析，表示理论和框架理论的基本工具，并通过示例将结果置于上下文中。
This article considers the relation between the spanning properties of lattice orbits of discrete series representations and the associated lattice co-volume. The focus is on the density theorem, which provides a trichotomy characterizing the existence of cyclic vectors and separating vectors, and frames and Riesz sequences. We provide an elementary exposition of the density theorem, that is based solely on basic tools from harmonic analysis, representation theory, and frame theory, and put the results into context by means of examples.
