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

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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 $R^d$ by translations.
5 pages, no figures, submitted to Amer. J. Math

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Classical Analysis and ODEs, 42B10

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http://salesiana.dossiersoluciones.com/handle/123456789/79455

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9911167
 http://arxiv.org/abs/math/9911167

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arXiv