Construction of the spectral expansion for singular β -Sturm-Liouville operators with certain applications
Abstract
Abstract In this paper, we investigate the β −Sturm-Liouville problem within the framework of a generalized quantum difference calculus, which extends Hahn’s difference operator to the half-line. Our primary focus is on establishing the existence of a spectral function associated with the β −Sturm-Liouville operator. In addition to this, we derive the Parseval identity corresponding to the problem. Furthermore, we obtain an explicit expansion formula in terms of these eigenfunctions.
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
Mathematical Analysis and Transform Methods
Quantum Mechanics and Non-Hermitian Physics
Publication details
- Journal / source
- Demonstratio Mathematica
- Publisher
- Walter de Gruyter GmbH
- Volume
- 59
- Issue
- 1
- Publication date
- 1 January 2026
- Language
- EN