Open Access Research Article

Jost Solution and the Spectrum of the Discrete Dirac Systems

Elgiz Bairamov*, Yelda Aygar and Murat Olgun

Author Affiliations

Department of Mathematics, Ankara University, Tandoğan, 06100 Ankara, Turkey

For all author emails, please log on.

Boundary Value Problems 2010, 2010:306571  doi:10.1155/2010/306571

Published: 29 November 2010

Abstract

We find polynomial-type Jost solution of the self-adjoint discrete Dirac systems. Then we investigate analytical properties and asymptotic behaviour of the Jost solution. Using the Weyl compact perturbation theorem, we prove that discrete Dirac system has the continuous spectrum filling the segment [-2,2]. We also study the eigenvalues of the Dirac system. In particular, we prove that the Dirac system has a finite number of simple real eigenvalues.