Hereditary completeness for systems of exponentials in weighted $L^2$-spaces

Abstract

We prove that for any weight $w$, which has at most polynomial decay at the endpoints of the interval, there exists a complete and minimal system $\{e^{iλ_n t}\}_{n\in \mathbb{N}}$ of exponentials in the weighted space $L^2(w)$ which is not hereditarily complete.