Mathematics > Classical Analysis and ODEs
[Submitted on 29 May 2018 (v1), last revised 14 Oct 2019 (this version, v3)]
Title:Fuglede's conjecture holds on cyclic groups $\mathbb{Z}_{pqr}$
View PDFAbstract:Fuglede's spectral set conjecture states that a subset $\Omega$ 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 $L^2(\Omega)$. We prove that Fuglede's conjecture holds on cyclic groups $\mathbb{Z}_{pqr}$ with $p,q,r$ distinct primes.
Submission history
From: Ruxi Shi [view email][v1] Tue, 29 May 2018 06:26:38 UTC (12 KB)
[v2] Mon, 23 Jul 2018 08:43:15 UTC (13 KB)
[v3] Mon, 14 Oct 2019 09:02:50 UTC (44 KB)
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