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

Year 2024, Volume: 16 Issue: 2, 299 - 308, 31.12.2024

Güler Başak Öznur

https://doi.org/10.47000/tjmcs.1438274

Abstract

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.

Keywords

Scattering function, Jost solution, asymptotic equation, hyperboic parameter, resolvent operator, continuous spectrum.

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