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Spectral properties of non-selfadjoint difference operators. (English) Zbl 0992.39018

The authors consider the operator L generated in 2 () by the difference expression (y) n =a n-1 y n-1 +b n y n +a n y n+1 , n, where {a n } n and {b n } n are complex sequences. The spectrum, the spectral singularities, and the properties of the principal vectors corresponding to the spectral singularities of L are investigated. The authors also study similar problems for the discrete Dirac operator generated in (, 2 ) by the system of the difference expression

Δy n (2) +p n y n (1) -Δy n-1 (1) +q n y n (2) ,

n, where {p n } n and {q n } n are complex sequences.

39A70Difference operators
39A12Discrete version of topics in analysis
34L05General spectral theory for OD operators