Completeness of the system of root functions of $q$-Sturm-Liouville operators

Abstract

In this paper, we study $q$-Sturm-Liouville operators. We constructa space of boundary values of the minimal operator and describe allmaximal dissipative, maximal accretive, self-adjoint and otherextensions of $q$-Sturm-Liouville operators in terms of boundaryconditions. Then we proved a theorem on completeness of the systemof eigenfunctions and associated functions of dissipative operatorsby using the Lidskii's theorem.