Riesz bases of exponentials for convex polytopes

Which domains in Euclidean space admit a basis of exponential functions? The answer 
depends on what we mean by a "basis". The best one can hope for is to have an orthogonal 
basis of exponentials, but it is well-known that many reasonable domains do not have such 
a basis. In this case, a Riesz basis is the next best thing one can hope for. I will 
discuss a recent result joint with Alberto Debernardi, which deals with the construction 
of Riesz bases of exponentials for convex polytopes in R^d.