On sufficient density conditions for lattice orbits of relative discrete series

Ulrik Enstad; Jordy Timo van Velthoven

doi:10.1007/s00013-022-01748-8

On sufficient density conditions for lattice orbits of relative discrete series

Ulrik Enstad, Jordy Timo van Velthoven^*

^*Corresponding author for this work

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Abstract

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

Original language	English
Pages (from-to)	279-291
Number of pages	13
Journal	Archiv der Mathematik
Volume	119
Issue number	3
DOIs	https://doi.org/10.1007/s00013-022-01748-8
Publication status	Published - 2022

Keywords

Density condition
Discrete series
Frame
Lattice
Riesz sequence

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AU - van Velthoven, Jordy Timo

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AB - 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.

KW - Density condition

KW - Discrete series

KW - Frame

KW - Lattice

KW - Riesz sequence

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ER -

On sufficient density conditions for lattice orbits of relative discrete series

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