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On sufficient density conditions for lattice orbits of relative discrete series

Journal Article (2022)
Author(s)

Ulrik Enstad (Stockholm University)

Jordy Timo Van Velthoven (TU Delft - Analysis)

Research Group
Analysis
Copyright
© 2022 Ulrik Enstad, J.T. van Velthoven
DOI related publication
https://doi.org/10.1007/s00013-022-01748-8
More Info
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Publication Year
2022
Language
English
Copyright
© 2022 Ulrik Enstad, J.T. van Velthoven
Research Group
Analysis
Issue number
3
Volume number
119
Pages (from-to)
279-291
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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.