Fuglede conjecture holds for convex planar domains

Abstract

Let $\Omega$ be a compact convex domain in the plane. We prove that $L^2(\Omega )$ has an orthogonal basis of exponentials if and only if $\Omega$ tiles the plane by translation.

Cited by in corpus (3)

• Fuglede's conjecture is false in 5 and higher dimensions
• Fuglede's conjecture fails in dimension 4
• Exponential bases on triangular domains