Principal Functions of Non-Selfadjoint Difference Operator with Spectral Parameter in Boundary Conditions

Abstract

We investigate the principal functions corresponding to the eigenvalues and the spectral singularities of the boundary value problem (BVP) $a_{n-1}{y}_{n-1}+b_n{y}_n+a_n{y}_{n+1}=\lambda y_n$ , $n\in \mathbb{N}$ and $({\gamma }_0+{\gamma }_1\lambda )y_1+({\beta }_0+{\beta }_1\lambda )y_0=0$, where $\left(a_n\right)$ and $\left(b_n\right)$ are complex sequences, $\lambda$ is an eigenparameter, and ${\gamma }_i$,${\beta }_i\in ℂ$ for $i=0$, 1.