Fugledeās spectral set conjecture for convex polytopes
Fugledeās spectral set conjecture for convex polytopes
Let $\Omega$ be a convex polytope in $\mathbb{R}^d$. We say that $\Omega$ is spectral if the space $L^2(\Omega)$ admits an orthogonal basis consisting of exponential functions. There is a conjecture, which goes back to Fuglede (1974), that $\Omega$ is spectral if and only if it can tile the space by ā¦