Methods and Applications of Analysis
Volume 16 (2009)
Completeness of Eigenfunctions of Sturm-Liouville Problems with Transmission Conditions
Pages: 299 – 312
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 $H$.
Eigenparameter-dependent boundary conditions; transmission conditions; eigenvalues; eigenfunctions; completeness
2010 Mathematics Subject Classification