2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79455We 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. MathClassical Analysis and ODEs42B10text