On sufficient density conditions for lattice orbits of relative discrete series

Journal article (2022)

Authors

Ulrik Enstad Stockholm University
J.T. van Velthoven Analysis - EEMCS
Research Group
Analysis (EEMCS) (TU Delft)
Copyright: © 2022 Ulrik Enstad, J.T. van Velthoven
DOI: https://doi.org/10.1007/s00013-022-01748-8
More Info
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Published Date

2022

Language

English

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Analysis

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.