The spectrum of the non-selfadjoint system of difference operators of first order

Abstract

Let L denote the operator generated in $ell_2 (N,C^2)$ by the difference express $ell(y)=lgroup^{a_{n+1}y^{(2)}_{n+1}+b_ny_n^{(2)}+p_ny_n^{(1)}}_{a_{n-1}y_{n-1}^{(1)}+b_ny_n^{(1)}+q_ny_n^{(2)}}rgroup, a_0=1,nin N={1,2,...}$ and the boundary condition $y_0^{(1)}=0$ where $(a_n)$, $(b_n)$, $(p_n)$ and $(q_n)$ are complex sequences and $a_nneq0$ , $b_nneq0$ for all $nin N$. In this paper we investigate the continuous spectrum, the eigenvalues and the spectral singularities of L.