@article{e90fc46c41c34f78b76f1fab4fde5401,
title = "Perturbation and spectral theory for singular indefinite Sturm–Liouville operators",
abstract = "We study singular Sturm–Liouville operators of the form [Formula presented] in L2((a,b);rj) with endpoints a and b in the limit point case, where, in contrast to the usual assumptions, the weight functions rj have different signs near a and b. In this situation the associated maximal operators become self-adjoint with respect to indefinite inner products and their spectral properties differ essentially from the Hilbert space situation. We investigate the essential spectra and accumulation properties of nonreal and real discrete eigenvalues; we emphasize that here also perturbations of the indefinite weights rj are allowed. Special attention is paid to Kneser type results in the indefinite setting and to L1 perturbations of periodic operators.",
keywords = "Discrete spectrum, Essential spectrum, Indefinite Sturm–Liouville operators, Periodic coefficients, Perturbations, Relative oscillation",
author = "Jussi Behrndt and Philipp Schmitz and Gerald Teschl and Carsten Trunk",
note = "Funding Information: The authors are indebted to the referee for a careful reading of the manuscript and various helpful comments to improve the presentation. J.B. gratefully acknowledges financial support by the Austrian Science Fund (FWF): P 33568-N. J.B. is also most grateful for the stimulating research stay and the hospitality at the University of Auckland in February and March 2023, where some parts of this paper were written. This publication is also based upon work from COST Action CA 18232 MAT-DYN-NET, supported by COST (European Cooperation in Science and Technology), www.cost.eu. Funding Information: Acknowledgements . The authors are indebted to the referee for a careful reading of the manuscript and various helpful comments to improve the presentation. J.B. gratefully acknowledges financial support by the Austrian Science Fund (FWF): P 33568-N. J.B. is also most grateful for the stimulating research stay and the hospitality at the University of Auckland in February and March 2023, where some parts of this paper were written. This publication is also based upon work from COST Action CA 18232 MAT-DYN-NET, supported by COST (European Cooperation in Science and Technology), www.cost.eu. Publisher Copyright: {\textcopyright} 2024 The Author(s)",
year = "2024",
month = oct,
day = "5",
doi = "10.1016/j.jde.2024.05.043",
language = "English",
volume = "405",
pages = "151--178",
journal = "Journal of Differential Equations",
issn = "0022-0396",
publisher = "ACADEMIC PRESS INC ELSEVIER SCIENCE",
}