Spectral properties of non-selfadjoint difference operators

Abstract

Let L denote the operator generated in ℓ2(ℤ) by the difference expression (ℓy)n= an-1yn-1+ bnyn+ anyn+1n ∈ ℤ = 0, ± 1, ± 2, where ann∈ℤand bnn∈ℤare complex sequences. In this paper we investigated the spectrum, the spectral singularities, and the properties of the principal vectors corresponding to the spectral singularities of L. We also studied similar problems for the discrete Dirac operator M generated in ℓ2(ℤ, ℂ2) by the system of difference expression Δ is the forward difference operator, i.e., Δyn(i)= yn+i(i)- yn(i)i = 1, 2, and pnn∈ℤare complex sequences. © 2001 Academic Press.