Convex bodies with a point of curvature do not have Fourier bases

Details Convex bodies with a point of curvature do not have Fourier bases Convex bodies with a point of curvature do not have Fourier bases

1999-11-23

arxiv.org/abs/math/9911167v2

Mathematics

Classical Analysis and ODEs

5 pages, no figures, submitted to Amer. J. Math

Scientific paper

We prove that no smooth symmetric convex body $\Omega$ 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 $\Omega$ can tile $R^d$ by translations.

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