Spectral properties of generalized eigenparameter dependent discrete Sturm-Liouville type equation

Abstract

Let L denote the non-selfadjoint difference operator of second order with boundary condition generated in ℓ2 (ℕ) by (Figure presented.) (Figure presented.) where {an}n∈ℕ and {bn}n∈ℕ are complex sequences, γi, βi ∈ ℂ, i = 0, 1, 2, …, p and λ is a eigenparameter. Discussing the spectral properties of L, we investigate the Jost function, spectrum, the spectral singularities, and the properties of the principal vectors corresponding to the spectral singularities of L, if (Figure presented.).