On sufficient density conditions for lattice orbits of relative discrete series

Ulrik Enstad, Jordy Timo van Velthoven*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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Abstract

This note provides new criteria on a unimodular group G and a discrete series representation (π, Hπ) of formal degree dπ> 0 under which any lattice Γ ≤ G with vol(G/Γ)dπ≤1 (resp. vol(G/Γ)dπ≥1) admits g∈ Hπ such that π(Γ) g is a frame (resp. Riesz sequence). The results apply to all projective discrete series of exponential Lie groups.

Original languageEnglish
Pages (from-to)279-291
Number of pages13
JournalArchiv der Mathematik
Volume119
Issue number3
DOIs
Publication statusPublished - 2022

Keywords

  • Density condition
  • Discrete series
  • Frame
  • Lattice
  • Riesz sequence

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