2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61263We prove that no ball admits a non-harmonic orthogonal basis of exponentials. We use a combinatorial result, originally studied by Erd\H os, which says that the number of distances determined by $n$ points in ${\Bbb R}^d$ is at least $C_d n^{\frac{1}{d}+ε_d}$, $ε_d>0$.Classical Analysis and ODEstext