Geodesic
Matrix difference equations with jump conditions and hyperbolic eigenparameter
Yelda Aygar1 ; Guler Basak Oznur1 ; Yelda Aygar ; Guler Basak Oznur
1Department of Mathematics, Gazi University, Ankara, Turkey
Acta mathematica Universitatis Comenianae, Tome 91 (2022) no. 2, pp. 149-159 
Yelda Aygar; Guler Basak Oznur; Yelda Aygar; Guler Basak Oznur. Matrix difference equations with jump conditions and hyperbolic eigenparameter. Acta mathematica Universitatis Comenianae, Tome 91 (2022) no. 2, pp. 149-159. http://geodesic.mathdoc.fr/item/AMUC_2022_91_2_a4/
@article{AMUC_2022_91_2_a4,
     author = {Yelda Aygar and Guler Basak Oznur and Yelda Aygar and Guler Basak Oznur},
     title = { Matrix difference equations with jump conditions and hyperbolic eigenparameter},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {149--159},
     year = {2022},
     volume = {91},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2022_91_2_a4/}
}
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Problems of difference equations with jump (discontinuity) conditions have an important role for many branches of sciences. They can be used to model a wide range of real-world applications such as heating, massing in physics, bursting rhythm models in medicine, optimal control models in economics and so on. In this paper, we consider some spectral and scattering properties of matrix difference equations with jump conditions and hyperbolic eigenparameter. Using the asymptotic behavior of Jost function, we find eigenvalues, spectral singularities, resolvent operator and spectrum of this problem. Also, we investigate scattering matrix and get some properties of scattering matrix. Finally, we present an example about the scattering matrix and the existence of eigenvalues in special cases.