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Eigenparameter dependent discrete Dirac equations with spectral singularities. (English) Zbl 1191.39005

The authors consider the discrete boundary value problem (BVP)

a n-1 y n-1 +b n y n +a n y n+1 =λy n ,n={1,2,},y 0 =0,

where (a n ) and (b n ) are complex sequences, a 0 0 and λ is a spectral parameter. They prove that the spectrum of the BVP consists of the continuous spectrum, the eigenvalues and the spectral singularities. They show that spectral singularities are poles of the resolvent and those are also embedded in the continuous spectrum, but indicating that they are not eigenvalues.

39A12Discrete version of topics in analysis
81Q05Closed and approximate solutions to quantum-mechanical equations
34L05General spectral theory for OD operators
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