Tiling by lattices for locally compact abelian groups

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 $L^2(Ω).$ The proof uses simple techniques from Harmonic Analysis.

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