Principal functions of non-selfadjoint difference operator with spectral parameter in boundary conditions. (English) Zbl 1220.39009

Summary: We investigate the principal functions corresponding to the eigenvalues and the spectral singularities of the boundary value problem \(a_{n-1}y_{n-1} + b_ny_n + a_ny_{n+1} = \lambda y_n\), \(n \in \mathbb N\) and \((\gamma_0 + \gamma_1 \lambda)y_1 + (\beta_0 + \beta_1 \lambda)y_0 = 0\), where \((a_n)\) and \((b_n)\) are complex sequences, \(\lambda\) is an eigenparameter, and \(\gamma_i, \beta_i \in \mathbb C\) for \(i = 0, 1\).


39A12 Discrete version of topics in analysis
39A06 Linear difference equations
39A45 Difference equations in the complex domain
34L05 General spectral theory of ordinary differential operators
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