2015/10/08 by Yelda Aygar, Aygar, Yelda, Elgiz Bairamov +3
Mathematics · Physics and Astronomy · #Spectral Theory in Mathematical Physics #Algebraic and Geometric Analysis #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1510.02218
In this paper, we find a polynomial-type Jost solution of a self-adjoint matrix-valued discrete Dirac system. Then we investigate analytical properties and asymptotic behavior of this Jost solution. Using the Weyl compact perturbation theorem, we prove that matrix-valued discrete Dirac system has continuous spectrum filling the segment [-2,2]. Finally, we examine the properties of the eigenvalues of this Dirac system and we prove that it has a finite number of simple real eigenvalues.