Perturbed discrete Sturm-Liouville problems and associated sampling theorems (Q1047536)

The aim of the paper is to investigate spectral properties of perturbed second-order difference operators. The underlying eigenvalue problem has the form \[ \nabla[p(n)\Delta y(n)]+ q(n)y(n)+ \sum_{i=1}^N r(n) r(i) y(i)= \lambda y(n). \] In a sequence of lemmata the authors present results about selfadjointness, Green's function, uniqueness of solutions, multiplicity of eigenvalues, eigenfunction expansion, sampling representations. In a final section some examples illustrate the results.