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arXiv · 2302.01202

Linear independence of coherent systems associated to discrete subgroups

Ulrik Enstad·Jordy Timo van Velthoven
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Abstract

This note considers the finite linear independence of coherent systems associated to discrete subgroups. We show by simple arguments that such coherent systems of amenable groups are linearly independent whenever the associated twisted group ring does not contain any nontrivial zero divisors. We verify the latter for discrete subgroups in nilpotent Lie groups. For the particular case of time-frequency translates of Euclidean space, our approach provides a simple and self-contained proof of the Heil--Ramanathan--Topiwala (HRT) conjecture for subsets of arbitrary discrete subgroups.

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Ulrik Enstad, Jordy Timo van Velthoven. 2023-02-02. Linear independence of coherent systems associated to discrete subgroups. https://arxiv.org/abs/2302.01202

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