DOI: 10.29132/ijpas.1908033 ISSN: 2149-0910

Spectrum of the Non-self-adjoint and Non-homogeneous Sturm-Liouville Operators with a Singular Potential

Cem Koşar, Nida Palamut Koşar
Show PDF Cite
In this paper we discuss in detail the quantitative properties of the spectrum of the non-self-adjoint and non-homogeneous Sturm Liouville Operators with a singular potential. The problem is formulated on the half-line and is supplemented by a boundary condition imposed at the origin, which reflects and accommodates the singular nature of the potential term. Special attention is given to the analytical structure of the spectrum under these conditions. In particular, we study the eigenvalues and spectral singularities in depth and establish a robust sufficient condition ensuring the finiteness of the eigenvalues, spectral singularities, and their respective multiplicities with this operator theoretic framework.

More from our Archive