Jost solutions and the spectrum of the system of difference equations. (Q1767170)

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 \(a_n\neq 0\), \(b_n\neq 0\). 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.