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Non-symmetric convex domains have no basis of exponentials

Mihail N. Kolountzakis
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Abstract

A conjecture of Fuglede states that a bounded measurable set $Ω$ in space, of measure 1, can tile space by translations if and only if the Hilbert space $L^2(Ω)$ has an orthonormal basis consisting of exponentials. If $Ω$ has the latter property it is called spectral. We generalize a result of Fuglede, that a triangle in the plane is not spectral, proving that every non-symmetric convex domain is not spectral.

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Mihail N. Kolountzakis. 1999-12-18. Non-symmetric convex domains have no basis of exponentials. https://arxiv.org/abs/math/9904064

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