Leptin densities in amenable groups

13.10.2021 10:45 - 12:00

Christoph Richard (Universität Erlangen)

We define a notion of uniform density on translation bounded measures in unimodular amenable locally compact Hausdorff groups, which is based on a group invariant introduced by Leptin in 1966. We show that this density notion coincides with the Banach density. We illustrate uselfulness of Leptin densities for a geometric proof of the model set density formula, which expresses the density of a uniform regular model set in terms of the volume of its window. This is based on joint work with Felix Pogorzelski (Leipzig) and Nicolae Strungaru (Edmonton), see https://arxiv.org/abs/2107.04760


M. Ehler, KH. Gröchenig

SR 12, 2. OG, OMP 1