Fuglede's conjecture holds on cyclic groups $\mathbb{Z}_{pqr}$
Discrete analysis (2019)
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Fuglede's spectral set conjecture states that a subset $Ω$ of a locally compact abelian group $G$ tiles the group by translation if and only if there exists a subset of continuous group characters which is an orthogonal basis of $L^2(Ω)$. We prove that Fuglede's conjecture holds on cyclic groups $\mathbb{Z}_{pqr}$ with $p,q,r$ distinct primes.
@article{DAS_2019_a6,
author = {Ruxi Shi},
title = {Fuglede's conjecture holds on cyclic groups $\mathbb{Z}_{pqr}$},
journal = {Discrete analysis},
year = {2019},
language = {en},
url = {http://geodesic.mathdoc.fr/item/DAS_2019_a6/}
}
Ruxi Shi. Fuglede's conjecture holds on cyclic groups $\mathbb{Z}_{pqr}$. Discrete analysis (2019). http://geodesic.mathdoc.fr/item/DAS_2019_a6/