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arXiv · 1508.04208

Tiling by lattices for locally compact abelian groups

Davide Barbieri·Eugenio Hernández·Azita Mayeli
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Abstract

For a locally compact abelian group $G$ a simple proof is given for the known fact that a bounded domain $\Omega$ tiles $G$ with translations by a lattice $\Lambda$ if and only if the set of characters of $G$ indexed by the dual lattice of $\Lambda$ is an orthogonal basis of $L^2(\Omega).$ The proof uses simple techniques from Harmonic Analysis.

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Davide Barbieri, Eugenio Hernández, Azita Mayeli. 2015-08-18. Tiling by lattices for locally compact abelian groups. https://arxiv.org/abs/1508.04208

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