Riesz bases of exponentials and the Bohr topology

We provide a necessary and sufficient condition to ensure that multi-tile ? ? mathvariant="double-struck">R d \Omega \subset \mathbb {R}^{d} of positive measure (but not necessarily bounded) admits structured Riesz basis exponentials for alttext="upper L squared left-parenthesis normal right-parenthesis"> L 2 ( stretchy="false">) encoding="application/x-tex">L^{2}(\Omega ) . New examples are given this characterization is generalized abstract locally compact abelian groups.