"Reproducing properties of lattice orbits of nilpotent Lie groups"Enstad, UlrikThe frame property of Gabor systems and its relation to the density of the underlying point set is a classical topic in time-frequency analysis. As is well-known, Gabor systems arise naturally from the Schrödinger representation of the Heisenberg group. This observation has in recent years inspired generalizations of time-frequency analysis to function systems arising from representations of nilpotent Lie groups. In this talk I will present sufficient density conditions for the existence of frames and Riesz sequences in lattice orbits of nilpotent Lie groups with smooth windows. The conditions involve the product of lattice co-volume and formal dimension, and complement Balian-Low type theorems for the non-existence of smooth frames and Riesz sequences at the critical density. The proof hinges on recent advances in the field of operator algebras, specifically the classification programme for nuclear C*-algebras. The talk is based on joint work with Erik Bédos and Jordy Timo van Velthoven. |
« back