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) 𝑎𝑛−1𝑦𝑛−1+𝑏𝑛𝑦𝑛+𝑎𝑛𝑦𝑛+1=𝜆𝑦𝑛, 𝑛∈ℕ and (𝛾0+𝛾1𝜆)𝑦1+(𝛽0+𝛽1𝜆)𝑦0=0, where (𝑎𝑛) and (𝑏𝑛) are complex sequences, 𝜆 is an eigenparameter, and 𝛾𝑖, 𝛽𝑖∈ℂ for 𝑖=0, 1.