Completeness of the Eigenvectors of a Dissipative Second Order Difference Operator: Dedicated To Lynn Erbe on the Occasion of His 65th Birthday

Abstract

In this paper we consider a dissipative linear operator generated in the Hilbert space l(2) by a second order difference expression on the semi-axis (in other words, by an infinite Jacobi matrix) in the Weyl-Hamburger limit-circle case. This operator is constructed via a boundary condition at infinity. We prove the completeness in 2 of the system of eigenvectors and associated vectors of the dissipative operator which is considered.