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J. Funct. Anal. 254-6, 1702-1720 (2008) [DOI: 10.1016/j.jfa.2007.10.007]

Relative Oscillation Theory for Sturm-Liouville Operators Extended

Helge Krüger and Gerald Teschl

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.

MSC2000: Primary 34B24, 34C10; Secondary 34L15, 34L05
Keywords: Sturm-Liouville operators, oscillation theory, spectral shift function

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