Jost Solution and the Spectrum of the Discrete Dirac Systems
Department of Mathematics, Ankara University, Tandoğan, 06100 Ankara, Turkey
Boundary Value Problems 2010, 2010:306571 doi:10.1155/2010/306571Published: 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.