Spectral analysis of singular ordinary differential operators with indefinite weights. (English) Zbl 1197.34167
The authors develop a perturbation approach to investigate spectral problems for singular ordinary differential operators with indefinite weight functions. They prove a general perturbation result on the local spectral properties of selfadjoint operators in Krein spaces which differ only by finitely many dimensions from the orthogonal sum of a fundamentally reducible operator and an operator with finitely many negative squares. This result is applied to singular indefinite Sturm-Liouville operators and higher order singular ordinary differential operators with indefinite weight functions.
Reviewer: Bilender P. Allahverdiev (Isparta)
MSC:
| 34L05 | General spectral theory of ordinary differential operators |
| 34B09 | Boundary eigenvalue problems for ordinary differential equations |
| 34B24 | Sturm-Liouville theory |
| 34B40 | Boundary value problems on infinite intervals for ordinary differential equations |
| 47E05 | General theory of ordinary differential operators |
| 34B20 | Weyl theory and its generalizations for ordinary differential equations |
Keywords:
Sturm-Liouville operator; ordinary differential operator; indefinite weight; Krein space; definitizable operator; critical point; finite rank perturbation; Titchmarsh-Weyl theoryReferences:
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