A functional model, eigenvalues, and finite singular critical points for indefinite Sturm-Liouville operators

Details A functional model, eigenvalues, and finite singular critical points for indefinite Sturm-Liouville operators A functional model, eigenvalues, and finite singular critical points for indefinite Sturm-Liouville operators

2009-02-27

arxiv.org/abs/0902.4900v2

Operator Theory: Advances and Applications, 2010, Volume 203, 247-287

Mathematics

Spectral Theory

38 pages, Proposition 2.2 and its proof corrected, Remarks 2.5, 3.4, and 3.12 extended, details added in subsections 2.3 and 4

Scientific paper

10.1007/978-3-0346-0161-0_11

Eigenvalues in the essential spectrum of a weighted Sturm-Liouville operator are studied under the assumption that the weight function has one turning point. An abstract approach to the problem is given via a functional model for indefinite Sturm-Liouville operators. Algebraic multiplicities of eigenvalues are obtained. Also, operators with finite singular critical points are considered.

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