Convex bodies with a point of curvature do not have Fourier bases
Alex Iosevich, Nets Hawk Katz, Terence Tao
Abstract
We prove that no smooth symmetric convex body Ω with at least one point of non-vanishing Gaussian curvature can admit an orthogonal basis of exponentials. (The non-symmetric case was proven by Kolountzakis). This is further evidence of Fuglede's conjecture, which states that such a basis is possible if and only if Ω can tile Rd by translations.
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