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.

To appear in Journal of the European Mathematical Society (JEMS)

References in corpus (2)

• The Fuglede conjecture for convex domains is true in all dimensions
• Combining Riesz bases in $R^d$

Cited by in corpus (3)

• A note on exponential Riesz bases
• Interpolation by multivariate polynomials in convex domains
• Random periodic sampling patterns for shift-invariant spaces