Riesz bases of exponentials for convex polytopes with symmetric faces

We prove that for any convex polytope Q subset of 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.

Automated summary

We prove the existence of a Riesz basis of exponential functions in the space L-2(Omega) for any centrally symmetric convex polytope Q in R-d, where all faces of Q in all dimensions are also centrally symmetric. This result is new for any dimension d greater than one.