Completeness of eigenfunctions of Sturm-Liouville problems with discontinuities at three points
Functional Analysis
2012-02-28 v2 Classical Analysis and ODEs
Abstract
In this work, we study discontinuous Sturm-Liouville type problems with eigenparameter dependent boundary condition and transmission conditions at three interior points. 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 eigenvalues of the problem are analytically simple, and the eigenfunctions of A are complete in H.
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Cite
@article{arxiv.1202.4858,
title = {Completeness of eigenfunctions of Sturm-Liouville problems with discontinuities at three points},
author = {Erdoğan Şen},
journal= {arXiv preprint arXiv:1202.4858},
year = {2012}
}
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15 pages