Methods and Applications of Analysis

Completeness of Eigenfunctions of Sturm-Liouville Problems with Transmission Conditions

Aiping Wang, Jiong Sun, Xiaoling Hao, and Siqin Yao

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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

Permanent link to this document
https://projecteuclid.org/euclid.maa/1273002794

Mathematical Reviews number (MathSciNet)
MR2650798

Zentralblatt MATH identifier
1210.34123

Subjects
Primary: 34L10: Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions 47E05: Ordinary differential operators [See also 34Bxx, 34Lxx] (should also be assigned at least one other classification number in section 47)

Keywords
Eigenparameter-dependent boundary conditions transmission conditions eigenvalues eigenfunctions completeness

Citation

Wang, Aiping; Sun, Jiong; Hao, Xiaoling; Yao, Siqin. Completeness of Eigenfunctions of Sturm-Liouville Problems with Transmission Conditions. Methods Appl. Anal. 16 (2009), no. 3, 299--312. https://projecteuclid.org/euclid.maa/1273002794


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