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

Abstract EN

Let L denote the operator generated in ℓ2(ℕ,ℂ2) by an+1yn+1(2)+bnyn(2)+pnyn(1)=λyn(1), an-1yn-1(1)+bnyn(1)+qnyn(2)=λyn(2), n∈ℕ, and the boundary condition (γ0+γ1λ)y1(2)+(β0+β1λ)y0(1)=0, where (an), (bn), (pn), and (qn), n∈ℕ are complex sequences, γi,βi∈ℂ, i=0,1, and λ is an eigenparameter.

In this paper we investigated the principal functions corresponding to the eigenvalues and the spectral singularities of L.