Yelda Aygar

Jost Solution and the Spectrum of the Discrete Dirac Systems

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.

Jost solution and the spectral properties of the matrix-valued difference operators

Abstract In this paper, we find polynomial type Jost solution of the selfadjoint matrix-valued difference equation of second order. Then we investigate analytical properties and asymptotic behaviour of the Jost solution. Using the Weyl compact perturbation theorem we prove that, the selfadjoint operator L generated by the matrix-valued difference expression of second order has the continuous spectrum filling the segment [ - 2 , 2 ] . We also study the eigenvalues of L and prove that it has a finite number of simple real eigenvalues.

Investigation of the spectrum and the Jost solutions of discrete Dirac system on the whole axis

AbstractWe consider the boundary value problem (BVP) for the discrete Dirac equations {yn+1(2)−yn(2)+pnyn(1)=λyn(1),yn−1(1)−yn(1)+qnyn(2)=λyn(2),n∈Z={0,±1,±2,…};y0(1)=0, where (pn) and (qn), n∈Z are real sequences, and λ is an eigenparameter. We find a polynomial type Jost solution of this BVP. Then we investigate the analytical properties and asymptotic behavior of the Jost solution. Using the Weyl compact perturbation theorem, we prove that a self-adjoint discrete Dirac system has a continuous spectrum filling the segment [−2,2]. We also prove that the Dirac system has a finite number of real eigenvalues.

Principal Functions of Nonselfadjoint Discrete Dirac Equations with Spectral Parameter in Boundary Conditions

Let denote the operator generated in by , , , and the boundary condition , where , , , and , are complex sequences, , , and is an eigenparameter. In this paper we investigated the principal functions corresponding to the eigenvalues and the spectral singularities of .

Principal Functions of Non-Selfadjoint Difference Operator with Spectral Parameter in Boundary Conditions

We investigate the principal functions corresponding to the eigenvalues and the spectral singularities of the boundary value problem (BVP) 𝑎𝑛−1𝑦𝑛−1

A note on spectral properties of a Dirac system with matrix coefficient

In this paper, we find a polynomial-type Jost solution of a self-adjoint matrix-valued discrete Dirac system. Then we investigate analytical properties and asymptotic behavior of this Jost solution. Using the Weyl compact perturbation theorem, we prove that matrix-valued discrete Dirac system has continuous spectrum filling the segment [−2, 2]. Finally, we examine the properties of the eigenvalues of this Dirac system and we prove that it has a finite number of simple real eigenvalues. c ©2017 All rights reserved.

Principal Vectors of Matrix-Valued Difference Operators

In this paper, we investigate the principal vectors corresponding to the eigenvalues and the spectral singularities of matrix-valued difference operator and get some properties of these vectors.