The Determinants of Perturbation Connected with a Dissipative Sturm-Liouville Operator

In this paper, the determinants of perturbation connected with a dissipative operator generated by the Sturm-Liouville differential expression on the half-line in the Weyl′s limit-circle case are investigated. An application is given to the problem of completeness of the system of eigenvectors and associated vectors of this operator.