Jost Solution and the Spectrum of the Discrete Dirac Systems

Elgiz Bairamov, Yelda Aygar, and Murat Olgun Department of Mathematics, Ankara University, Tandoğan, 06100 Ankara, Turkey Correspondence should be addressed to Elgiz Bairamov, [email protected] Received 14 September 2010; Accepted 10 November 2010 Academic Editor: Raul F. Manasevich Copyright q 2010 Elgiz Bairamov et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 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.