Riesz basis property of discontinuous Sturm–Liouville problem with transmission condition rationally dependent on the eigenparameter
Abstract
This paper investigates a discontinuous Sturm–Liouville problem in which the boundary conditions depend linearly on the eigenparameter and the transmission conditions depend rationally on it. We show that the eigenvalues are real and form a discrete set, and that the system of weak eigenfunctions constitutes a Riesz basis for the underlying Hilbert space. A lower bound for the eigenvalues is also derived. The analysis relies on operator-pencil theory.
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
Differential Equations and Boundary Problems
Mathematical Analysis and Transform Methods
Publication details
- Journal / source
- Integral Transforms and Special Functions
- Pages
- 1–17
- Publication date
- 10 January 2026
- Language
- EN