Investigation of the Spectrum of Nonself-Adjoint Discontinuous Sturm-Liouville Operator

Year 2024, , 119 - 130, 24.09.2024

Özge Akçay , Nida Palamut Koşar

https://doi.org/10.36753/mathenot.1410536

Abstract

In this paper, we study nonself-adjoint Sturm-Liouville operator containing both the discontinuous coefficient and discontinuity conditions at some point on the positive half-line. The eigenvalues and the spectral singularities of this problem are examined and it is proved that this problem has a finite number of spectral singularities and eigenvalues with finite multiplicities under two different additional conditions. Furthermore, the principal functions corresponding to the eigenvalues and the spectral singularities of this operator are determined.

Keywords

Discontinuous coefficient, Discontinuity conditions, Eigenvalues and spectral singularities, Nonself-adjoint Sturm-Liouville operator, Principal functions

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