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Zbl 1072.39013
Bairamov, E.; Coskun, C.
Jost solutions and the spectrum of the system of difference equations.
(English)
[J] Appl. Math. Lett. 17, No. 9, 1039-1045 (2004). ISSN 0893-9659

The authors study the first order nonself-adjoint system of difference equations $a_{n+1}y_{n+1}^{(2)}+b_ny_n^{(2)}+p_ny_n^{(1)}=\lambda y_n^{(1)}$, $a_{n-1}y_{n-1}^{(1)}+b_ny_n^{(1)}+q_ny_n^{(2)}=\lambda y_n^{(2)}$, where the coefficients are complex sequences with $a_n\ne 0$, $b_n\ne 0$. The concept of the so-called Jost solution is introduced for this system. The study of its properties then serves to obtain information about eigenvalues and spectral singularities of the discrete system.
[Pavel Rehak (Brno)]
MSC 2000:
*39A12 Discrete version of topics in analysis
34L05 General spectral theory for ODE

Keywords: difference equation; spectral analysis; spectral singularity; Jost solution; eigenvalues; discrete system

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