Let S be a bounded, Riemann measurable set in Rd, and Λ be a lattice. By a theorem of Fuglede, if S tiles Rd with translation set Λ, then S has an orthogonal basis of exponentials. We show that, under the more general condition that S multi-tiles Rd with translation set Λ, S has a Riesz basis of exponentials. The proof is based on Meyer's quasicrystals.
- Riesz bases