Spectral Analysis of an Operator with Fourier-Neumann Expansions Beneath

Abstract

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