The spectrum of discrete Dirac operator with a general boundary condition

In this paper, we aim to investigate the spectrum of the nonselfadjoint operator L generated in the Hilbert space l 2 ( N , C 2 ) by the discrete Dirac system { y n + 1 ( 2 ) − y n ( 2 ) + p n y n ( 1 ) = λ y n ( 1 ) , − y n ( 1 ) + y n − 1 ( 1 ) + q n y n ( 2 ) = λ y n ( 2 ) , n ∈ N , and the general boundary condition ∑ n = 0 ∞ h n y n = 0 , where λ is a spectral parameter, Δ is the forward difference operator, ( h n ) is a complex vector sequence such that h n = ( h n ( 1 ) , h n ( 2 ) ) , where h n ( i ) ∈ l 1 ( N ) ∩ l 2 ( N ) , i = 1 , 2 , and h 0 ( 1 ) ≠ 0 . Upon determining the sets of eigenvalues and spectral singularities of L , we prove that, under certain conditions, L has a finite number of eigenvalues and spectral singularities with finite multiplicity.