Ask a Question

Prefer a chat interface with context about you and your work?

Fugledeā€™s spectral set conjecture for convex polytopes

Fugledeā€™s 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€¦