Abstract
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-tilesRd with translation set Λ, S has a Riesz basis of exponentials. The proof is based on Meyerʼs quasicrystals.
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