Some scattering and spectral properties of eigenparameter dependent quantum difference equations with matrix value impulsive conditions

Abstract

In this study, we present a problem which consists quantum difference equation with matrix value impulsive conditions and eigenparameter dependent boundary condition. Our examination is based on the concept of main spectral and scattering properties of this problem. We introduce Jost solution, Jost function and scattering function of the problem. Then, we find resolvent operator, Green function, eigenvalues and continuous spectrum of the operator generated by same problem.