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Zbl 1191.39005
Bairamov, Elgiz; Koprubasi, Turhan
Eigenparameter dependent discrete Dirac equations with spectral singularities. (English)
[J] Appl. Math. Comput. 215, No. 12, 4216-4220 (2010). ISSN 0096-3003

The authors consider the discrete boundary value problem (BVP) $$a_{n-1}y_{n-1}+ b_ny_n+ a_ny_{n+1}=\lambda y_n, \quad n\in \Bbb N= \{1, 2,\dots\},\quad y_0 = 0,$$ where $(a_n)$ and $(b_n)$ are complex sequences, $a_0 \neq 0$ and $\lambda$ 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.
[Haydar Akca (Al Ain)]

MSC 2000:: *39A12 Discrete version of topics in analysis
81Q05 Closed and approximate solutions to quantum-mechanical equations
34L05 General spectral theory for ODE

Keywords: discrete Dirac equations; spectral analysis; discrete spectrum; spectral singularities; discrete boundary value problem; resolvent

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