A dynamical approach to density theorems for sampling in unimodular groups

18.01.2023, 13:00  –  Haus 9, Raum 0.17 und Zoom
Forschungsseminar Diskrete Spektraltheorie

Dr. Ulrik Enstad (Stockholm University)

Abstract: Many structured function systems in harmonic analysis arise from the action of a unitary group representation on a single vector in the underlying Hilbert space. A central question is whether the spanning properties of such systems are retained when sampling from a discrete subset instead of the whole group. Intuitively this should depend on the "size" or "density" of the discrete subset, and in many situations, so-called density theorems formalize this intuition. In this talk, I will present joint work with Sven Raum, showing how notions from aperiodic order can be used to give a unified proof of many different density theorems in the literature.