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arXiv · 2610.03200

A Balian-Low theorem for nilpotent Lie groups

Ulrik Enstad·Jordy Timo van Velthoven
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Abstract

We prove strict necessary density conditions for smooth coherent frames and Riesz sequences in the orbit of a connected, simply connected, nilpotent Lie group. This extends previous results for homogeneous groups to general nilpotent Lie groups. The main novelty in our approach is that we prove a stability result for coherent frames and Riesz sequences based on deforming their representation rather than their index set.

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Ulrik Enstad, Jordy Timo van Velthoven. 2026-10-02. A Balian-Low theorem for nilpotent Lie groups. https://arxiv.org/abs/2610.03200

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