Some Scattering and Spectral Properties of a Difference Equation with an Interface Condition and Hyperbolic Eigenparameter

The purpose aim of this study is to investigate the properties of scattering solutions and the scattering function of an difference equation with the interface conditions and hyperbolic parameter. We also investigate resolvent operator, Green function, continuous spectrum and the set of the eigenvalues of this problem. Finally, we present an example to demonstrate the application of our results. This work is important because the boundary condition is depend on quadratic hyperbolic parameter. This difference provides a new perspective of the problem.