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Zbl 0992.39018
Adivar, Murat; Bairamov, Elgiz
Spectral properties of non-selfadjoint difference operators.
(English)
[J] J. Math. Anal. Appl. 261, No.2, 461-478 (2001). ISSN 0022-247X

The authors consider the operator $L$ generated in $\ell^2({\Bbb Z})$ by the difference expression $(\ell y)_n=a_{n-1}y_{n-1}+b_ny_n+a_ny_{n+1}$, $n\in{\Bbb Z}$, where $\{a_n\}_{n\in{\Bbb Z}}$ and $\{b_n\}_{n\in{\Bbb Z}}$ 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 $\ell({\Bbb Z,\Bbb C}^2)$ by the system of the difference expression $$\pmatrix \Delta y_n^{(2)}+p_ny_n^{(1)}\cr -\Delta y_{n-1}^{(1)}+q_ny_n^{(2)} \endpmatrix,$$ $n\in{\Bbb Z}$, where $\{p_n\}_{n\in{\Bbb Z}}$ and $\{q_n\}_{n\in{\Bbb Z}}$ are complex sequences.
[Pavel Rehak (Brno)]
MSC 2000:
*39A70 Difference operators
39A12 Discrete version of topics in analysis
34L05 General spectral theory for ODE

Keywords: non-selfadjoint difference operator; spectrum; spectral singularities; principal vectors; discrete Dirac operator

Cited in: Zbl 1025.39001

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