Ulrik Enstad: A dynamical approach to sampling and interpolation in unimodular groups

Abstract

I will present some joint work with Sven Raum on sampling and interpolation in general unimodular locally compact groups. One of the main contributions is a new notion of covolume for point sets in such groups that simultaneously generalizes the covolume of a lattice and the reciprocal of the Banach/Beurling density for amenable groups. This notion of covolume arises naturally from the transverse measure theory of the associated hull dynamical system of a point set. The sampling and interpolation results are obtained by considering an étale groupoid associated to a point set whose groupoid C*-algebra generalizes the group C*-algebra in the lattice case.