Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Jost Solution and the Spectrum of the Discrete Dirac Systems | Hindawi Publishing Corporation Boundary Value Problems Volume 2010 Article ID 306571 11 pages doi 2010 306571 Research Article Jost Solution and the Spectrum of the Discrete Dirac Systems Elgiz Bairamov Yelda Aygar and Murat Olgun Department of Mathematics Ankara University Tandogan 06100 Ankara Turkey Correspondence should be addressed to Elgiz Bairamov bairamov@ Received 14 September 2010 Accepted 10 November 2010 Academic Editor Raul F. Manasevich Copyright 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. 1. Introduction Let us consider the boundary value problem BVP generated by the Sturm-Liouville equation -y q x y A2y 0 x TO and the boundary condition y 0 0 where q is a real-valued function and A EC is a spectral parameter. The bounded solution of satisfying the condition lim y x A e iAx 1 A eC A A e c Im A 0 x TO 2 Boundary Value Problems will be denoted by e x 1 . The solution e x 1 satisfies the integral equation e x 1 ei1x J sm 1x q t e t 1 dt. It has been shown that under the condition TO x q x dx TO 0 the solution e x 1 has the integral representation e x 1 ei1x f K x t eiUdt 1 eC x where the function K x t is defined by q. The function e x 1 is analytic with respect to 1 in c 1 1 EC Im 1 0 continuous c and e x 1 ei1x 1 o 1 1 eC x TO holds 1 chapter 3 . The functions
