Principal functions of Nonselfadjoint discrete Dirac equations with spectral parameter in boundary conditions

Abstract

Let L denote the operator generated in ℓ 2 (ℕ, ℂ 2) by a n+1 y n+1(2) + b ny n(2) + p ny n(1) = λ y n(1), a n-1y n-1(1) + b ny n(1) + q ny n(2) = λ y n(2), n ∈ ℕ, and the boundary condition (γ 0 + γ 1λ) y 1(2) + (β 0 + β 1λ) y 0(1) = 0, where (a n), (b n), (p n), and (q n), n ∈ ℕ are complex sequences, γ i, β i ∈ 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. © 2012 Yelda Aygar et al.