05652722

j

05652722 Annaby, M.H. Hassan, H.A. El-Haddad, O.H. Perturbed discrete Sturm-Liouville problems and associated sampling theorems. Rocky Mt. J. Math. 39, No. 6, 1781-1807 (2009). 2009 Rocky Mountain Mathematics Consortium, Arizona State University, Tempe, AZ EN Green's function sampling theory rank one perturbations discrete Sturm-Liouville problems spectral properties second-order difference operators eigenvalue problem eigenfunction expansion

doi:10.1216/RMJ-2009-39-6-1781

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. Stefan Hilger (Eichst\"att)