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.