Dissipative non-self-adjoint Sturm-Liouville operators and completeness of their eigenfunctions

In this paper, non-self-adjoint Sturm-Liouville operators in Weyl's limit-circle case are studied. We first determine all the non-self-adjoint boundary conditions yielding dissipative operators for each allowed Sturm-Liouville differential expression. Then, using the characteristic determinant, the completeness of the system of eigenfunctions and associated functions for these dissipative operators is proved.