Completeness of eigenfunctions of Sturm-Liouville problems with discontinuities at three points

Details Completeness of eigenfunctions of Sturm-Liouville problems with discontinuities at three points Completeness of eigenfunctions of Sturm-Liouville problems with discontinuities at three points

2012-02-22

arxiv.org/abs/1202.4858v2

Mathematics

Functional Analysis

15 pages

Scientific paper

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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