Riesz bases of exponentials for convex polytopes with symmetric faces

Abstract

We prove that for any convex polytope $\Omega \subset {\mathbb{R}}^d$ which is centrally symmetric and whose faces of all dimensions are also centrally symmetric, there exists a Riesz basis of exponential functions in the space $L^2(\Omega )$. The result is new in all dimensions $d$ greater than one.