A study of some discrete Dirac equations with principal functions

Abstract

Let L denote the operator generated in ℓ2(N, C2) by (Formula Presented.) and the boundary condition (Formula Presented.) where (an) , (bn) , (pn) and (qn) , n∈ N are complex sequences, γi, βi∈ C, i= 0 , 1 , 2 and λ is a eigenparameter. With respect to the spectral properties of L, we investigate the properties of the principal functions corresponding to the eigenvalues and the spectral singularities of L, if (Formula Presented.) holds for some ε> 0 and δ∈[12,1].