Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter

Abstract

Eigenfunctions expansion for discrete symplectic systems on a finite discrete interval is established in the case of a general linear dependence on the spectral parameter as a significant generalization of the Expansion theorem given by Bohner et al. (2009) [14]. Subsequently, an integral representation of the Weyl–Titchmarsh M(λ)-function is derived explicitly by using a suitable spectral function and a possible extension to the half-line case is discussed. The main results are illustrated by several examples.