Multi-tiling and Riesz bases
Classical Analysis and ODEs
2013-11-21 v2 Functional Analysis
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.
Keywords
Cite
@article{arxiv.1212.4679,
title = {Multi-tiling and Riesz bases},
author = {Sigrid Grepstad and Nir Lev},
journal= {arXiv preprint arXiv:1212.4679},
year = {2013}
}