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Open Access Open Badges 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

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

Published: 29 November 2010


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.