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Fuglede conjecture holds for convex planar domains

Alex Iosevich·Nets Katz·Terry Tao
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Abstract

Let $Ω$ be a compact convex domain in the plane. We prove that $L^2(Ω)$ has an orthogonal basis of exponentials if and only if $Ω$ tiles the plane by translation.

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Alex Iosevich, Nets Katz, Terry Tao. 2001-04-07. Fuglede conjecture holds for convex planar domains. https://arxiv.org/abs/math/0104087

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