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.
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
Holomorphic and Operator Theory
Differential Equations and Boundary Problems
Publication details
- Journal / source
- Boundary Value Problems
- Publisher
- Springer Science and Business Media LLC
- Volume
- 2026
- Issue
- 1
- Publication date
- 11 June 2026
- Language
- EN