## Methods and Applications of Analysis

### Completeness of Eigenfunctions of Sturm-Liouville Problems with Transmission Conditions

#### Abstract

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 $H$.

#### Article information

Source
Methods Appl. Anal., Volume 16, Number 3 (2009), 299-312.

Dates
First available in Project Euclid: 4 May 2010