Spectral Analysis of an Operator with Fourier-Neumann Expansions Beneath

We perform spectral analysis of a Sturm-Liouville operator on \(L^2(\mathbb {R}_+,dx)\) $L^2({\mathbb{R}}_{+},dx)$ which, through the Liouville transformation, is unitarily equivalent to the Schrödinger operator on \(L^2(\mathbb {R},dx)\) $L^2(\mathbb{R},dx)$ with heavy negative potential \(V(x)=-e^{2x}\) $V(x)=-e^{2x}$ . This analysis clarifies some operator theory aspects of the setting of Fourier-Neumann expansions initiated by Varona in 1994.