Relative Oscillation Theory for Sturm-Liouville Operators Extended

Helge Krueger; Gerald Teschl

doi:10.1016/j.jfa.2007.10.007

paper

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 $H u = r^{- 1} (- (p u^{'})^{'} + q u)$ 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

Relative Oscillation Theory for Sturm-Liouville Operators Extended

Abstract

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