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arXiv · 1805.11261

Fuglede's conjecture holds on cyclic groups $\mathbb{Z}_{pqr}$

Ruxi Shi
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Abstract

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.

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Ruxi Shi. 2019-10-14. Fuglede's conjecture holds on cyclic groups $\mathbb{Z}_{pqr}$. https://doi.org/10.19086/da.10570

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