On a non-self-adjoint Sturm–Liouville problem: spectral and inverse analysis

Abstract

In this paper, we study a Sturm–Liouville boundary value problem with a complex-valued potential represented by an absolutely convergent Fourier series. We construct fundamental solutions, define the characteristic function, and analyze the discrete spectrum. By extending the potential to the half-line, we introduce Jost-type solutions and derive the associated spectral coefficient. Furthermore, we investigate the Green function and resolvent operator, proving compactness and discreteness of the spectrum.