A Study of The Scattering Properties of Eigenparameter- Dependent Matrix Difference Operator With Transmission Condition


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Authors: G. B. ÖZNUR AND Y. AYGAR

DOI: 10.46793/KgJMat2603.479O

Abstract:

In this paper, we set a transmission boundary value problem for a matrix valued difference equation on the semi axis. The main purpose of this study is to examine the properties of scattering solutions and scattering functions of this problem. Firstly, by giving the Jost solution and scattering solutions of this problem, we obtain the Jost function and the scattering function of the problem. We also investigate eigenvalues, spectral singularities, resolvent operator and continuous spectrum of this problem.



Keywords:

Transmission condition, difference equation, eigenvalues, Jost function, spectral singularity, resolvent operator, scattering function.



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