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

Abstract

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.

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 4.2, section 6 rearranged, typos corrected, references added

References in corpus (5)

• The similarity problem for $J$-nonnegative Sturm-Liouville operators
• Spectral properties of singular Sturm-Liouville operators with indefinite weight sgn x
• Indefinite Sturm-Liouville operators with the singular critical point zero
• Abstract kinetic equations with positive collision operators
• Indefinite Sturm-Liouville operators $ (\sgn x) (- \frac{d^2}{dx^2} +q(x))$ with finite-zone potentials

Cited by in corpus (1)

• The similarity problem for indefinite Sturm-Liouville operators and the HELP inequality