THE COMPLETENESS OF EIGENFUNCTIONS OF PERTURBATION CONNECTED WITH STURM-LIOUVILLE OPERATORS

摘要

In this paper, non-self-adjoint Sturm-Liuville 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, we prove the completeness of the system of eigenfunctions and associated functions for these dissipative operators.