On sampling and interpolation by model sets

Christoph Richard, Christoph Schumacher

Published 2018-09-27Version 1

We re-analyse a result of Matei and Meyer on stable sampling for simple model sets. Our setting is model sets in locally compact second countable abelian groups and Fourier analysis of unbounded complex Radon measures as developed by Argabright and de Lamadrid. This yields an alternative proof of the underlying model set duality between sampling and interpolation. For rather general model sets, we also give an elementary proof of stable sampling and interpolation away from the critical density, which is based on the Poisson Summation Formula.