Effective Pruefer Angles and Relative Oscillation Criteria

Details Effective Pruefer Angles and Relative Oscillation Criteria Effective Pruefer Angles and Relative Oscillation Criteria

2007-09-03

arxiv.org/abs/0709.0127v2

J. Diff. Eq. 245, 3823-3848 (2008)

Mathematics

Spectral Theory

22 pages

Scientific paper

10.1016/j.jde.2008.06.004

We present a streamlined approach to relative oscillation criteria based on effective Pruefer angles adapted to the use at the edges of the essential spectrum. Based on this we provided a new scale of oscillation criteria for general Sturm-Liouville operators which answer the question whether a perturbation inserts a finite or an infinite number of eigenvalues into an essential spectral gap. As a special case we recover the Gesztesy-Uenal criterion (which works below the spectrum and contains classical criteria by Kneser, Hartman, Hille, and Weber) and the well-known results by Rofe-Beketov including the extensions by Schmidt.

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