The density theorem for discrete series representations restricted to lattices

José Luis Romero, Jordy Timo van Velthoven*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

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.

Original languageEnglish
JournalExpositiones Mathematicae
DOIs
Publication statusPublished - 2021

Keywords

  • Cyclic vector
  • Density condition
  • Discrete series representation
  • Frame
  • Lattice subgroup
  • Riesz sequence

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