Article
J. Math. Anal. Appl. 518, 126673 (2023) [DOI: 10.1016/j.jmaa.2022.126673]

Relative oscillation theory and essential spectra of Sturm-Liouville operators

Jussi Behrndt, Philipp Schmitz, Gerald Teschl, and Carsten Trunk

Abstract
We develop relative oscillation theory for general Sturm-Liouville differential expressions of the form
1/r (- d/ dx p d/ dx + q)
and prove perturbation results and invariance of essential spectra in terms of the real coefficients p, q, r. The novelty here is that we also allow perturbations of the weight function r in which case the unperturbed and the perturbed operator act in different Hilbert spaces.

MSC2020: Primary 34L05, 81Q10; Secondary 34L40, 47E05
Keywords: essential spectrum, Sturm-Liouville operators, perturbations, relative oscillation

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