Given a lattice Λ in a locally compact abelian group G and a
measurable subset Ω with finite and positive measure, then the set of
characters associated to the dual lattice form a frame for L2(Ω) if and
only if the distinct translates by Λ of Ω have almost empty
intersections. Some consequences of this results are the well-known Fuglede
theorem for lattices, as well as a simple characterization for frames of
modulates.Comment: note: results include as special case those of arXiv:1508.0420
