There are no Riesz bases of exponentials in balls and triangles

We prove that $L^2(Ω)$ admits no Riesz basis of exponentials when $Ω$ is a ball in $\R^n$, $n\geq2$, or a nondegenerate triangle in $\R^2$. The ball result extends to every nonempty bounded convex open set with $C^2$ boundary in $\R^n$, $n\geq2$. Starting from a hypothetical Riesz basis, we use Beur