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

Abstract

We prove that for every $0<\alpha <1$ there exists ${\Lambda }_{\alpha }\subset \mathbb{R}$ such that the system $\{e^{i\lambda t}{\}}_{\lambda \in {\Lambda }_{\alpha }}$ is complete and minimal, but not hereditarily complete in the weighted space $L^2(w)$ for any weight $w$ with $w(t)\asymp (\pi -|t|{)}^{\alpha }$ on $(-\pi ,\pi )$.

arXiv comment13 pages