Completeness of Eigenfunctions of Sturm-Liouville Problems with Transmission Conditions

• Autores: Aiping Wang, Jiong Sun, Xiaoling Hao, Siqin Yao
• Localización: Methods and applications of analysis, ISSN 1073-2772, Vol. 16, Nº 3, 2009, págs. 299-312
• Idioma: inglés
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• Resumen

  • 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.