Scattering theory of Impulsive sturm-Liouville operators

This thesis consists of five chapters. The first chapter is devoted to the Introduction. The second chapter includes the fundamental definitions and the theorems which are related to the topic. In the third chapter, Sturm-Liouville operator with spectral parameter dependent bo undary condition is considered on L2[0, ∞). Jost solution, Jost function and scattering function of this problem are obtained. Then, the properties of the scattering function are examined. Furthermore, set of eigenvalues, resolvent operator and the Green function of this operator are found. Finally, the obtained results are examined through an example. In the fourth chapter, the scattering theory of the impulsive discrete Dirac operator for which the boundary condition depending on the spectral parameter defined on the semi axis is examined and original results are obtained. In the last chapter, results obtained in this thesis are summarized and ideas regarding the implications and extensions of the conclusions are expressed.