Spectral analysis of singular ordinary differential operators with indefinite weights

In this paper we develop a perturbation approach to investigate spectral problems for singular ordinary differential operators with indefinite weight functions We prove a general perturbation result on the local spectral properties of selfadjoint operators in Krem spaces which differ only by finitely many dimensions from the orthogonal sum of a fundamentally reducible operator and ail 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 (C) 2009 Elsevier Inc All rights reserved