Resumen de Completeness of Eigenfunctions of Sturm-Liouville Problems with Transmission Conditions

Aiping Wang, Jiong Sun, Xiaoling Hao, Siqin Yao

• In this paper, we investigate a class of Sturm-Liouville problems with eigenparameter- dependent boundary conditions and transmission conditions at an interior point. A self-adjoint linear operator A is defined in a suitable Hilbert space H such that the eigenvalues of such a problem coincide with those of A. We show that the operator A has only point spectrum, the eigenvalues of the problem are algebraically simple, and the eigenfunctions of A are complete in H.