Riesz bases of exponentials and the Bohr topology

Abstract

We provide a necessary and sufficient condition to ensure that a multi-tile Ω ⊂ R d \Omega \subset \mathbb {R}^{d} of positive measure (but not necessarily bounded) admits a structured Riesz basis of exponentials for L 2 ( Ω ) L^{2}(\Omega ) . New examples are given and this characterization is generalized to abstract locally compact abelian groups.