Multi-tiling and Riesz bases
By Sigrid Grepstad, Nir Lev. 2012
79 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Materials Chemistry, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/c9d0d54d5c0fa9c8a6a2901009c92cf484566d6d
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In Geometry and Topology
In Materials Chemistry
In Numerical Analysis
Citations in the corpus
- Multiple lattice tiles and Riesz bases of exponentials (2013, methodology): “As an interesting corollary of Theorem 1 let us mention, as is done in [5], that, according to the recent result of [4], ifΩ is a centrally symmetric polytope inR, whose codimension 1 faces are also centrally symmetric and whose vertices all have rational coordinates, then L(2)(Ω) has a Riesz basis ”