Spectrum is rational in dimension one

Chun-Kit Lai, Yang Wang

A bounded measurable set $\Omega \subset {\mathbb{R}}^d$ is called a spectral set if it admits some exponential orthonormal basis $\{e^{2\pi i⟨\lambda ,x⟩}:\lambda \in \Lambda \}$ for $L^2(\Omega )$. In th…