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Relative Oscillation Theory for Sturm-Liouville Operators Extended

arXiv:0707.3451 · doi:10.1016/j.jfa.2007.10.007

Abstract

We extend relative oscillation theory to the case of Sturm--Liouville operators $H u = r^{-1}(-(pu')'+q u)$ with different $p$'s. We show that the weighted number of zeros of Wronskians of certain solutions equals the value of Krein's spectral shift function inside essential spectral gaps.

16 pages