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Jost solutions and the spectrum of the system of difference equations. (English) Zbl 1072.39013
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.

39A12Discrete version of topics in analysis
34L05General spectral theory for OD operators
Full Text: DOI
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