Spectral analysis of discontinuous Sturm-Liouville operators with Herglotzs transmission

Abstract

In this paper, we study the spectral properties of the Sturm-Liouville operator with eigenparameter-dependent boundary conditions and transmission conditions. In details, we introduce a Hilbert space formula, so that the problem we consider can be interpreted as an eigenvalue problem of an self-adjoint operator. Moreover, the Green's function and the resolvent of the related linear operator are obtained.

Keywords

• spectral analysis
• sturm-liouville operator
• transmission conditions
• eigenparameter dependent boundary condition
• eigenvalue problem