20 research outputs found
A functional model, eigenvalues, and finite singular critical points for indefinite Sturm-Liouville operators
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.Comment: 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 adde