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arXiv · 1212.4679

Multi-tiling and Riesz bases

Sigrid Grepstad·Nir Lev
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Abstract

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.

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Sigrid Grepstad, Nir Lev. 2013-11-20. Multi-tiling and Riesz bases. https://arxiv.org/abs/1212.4679

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