Linear independence of coherent systems associated to discrete subgroups

22.06.2023, 13:00 - 14:00  –  Haus 9, Raum 2.22
Forschungsseminar: Gruppen und Operatoralgebren

Ulrik Enstad (UP)

The HRT conjecture states that any finite set of time-frequency shifts of a nonzero, square-integrable function is linearly independent. While the conjecture is still open, it was settled by Linnell in the case where the time-frequency shifts belong to a discrete subgroup of R^d. In this talk I will present an elementary proof of Linnell's theorem which also extends to other settings, in particular to any coherent system arising from a projective discrete series of a simply connected, nilpotent Lie group.

The talk is based on recent joint work with Jordy Timo van Velthoven.