Tiling by lattices for locally compact abelian groups

2015/08/18 by Davide Barbieri, Barbieri, Davide, Eugenio Hernández +3 · 1 citation
Computer Science · Mathematics · #Cellular Automata and Applications #FOS: Mathematics #Functional Analysis (math.FA) #Group Theory (math.GR) #Mathematical Analysis and Transform Methods #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1508.04208

openalex publication_date 2015/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a locally compact abelian group G a simple proof is given for the known fact that a bounded domain Ω tiles G with translations by a lattice Λ if and only if the set of characters of G indexed by the dual lattice of Λ is an orthogonal basis of L²(Ω). The proof uses simple techniques from Harmonic Analysis.

Cited by

• Non-separable lattices, Gabor orthonormal bases and Tilings

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