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