2021
DOI: 10.48550/arxiv.2107.13850
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Smooth lattice orbits of nilpotent groups and strict comparison of projections

Erik Bédos,
Ulrik Enstad,
Jordy Timo van Velthoven

Abstract: This paper provides sufficient density conditions for the existence of smooth vectors generating a frame or Riesz sequence in the lattice orbit of a square-integrable projective representation of a nilpotent Lie group. The conditions involve the product of lattice co-volume and formal dimension, and complement Balian-Low type theorems for the nonexistence of smooth frames and Riesz sequences at the critical density. The proof hinges on a connection between smooth lattice orbits and generators for an explicitly… Show more

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