Relative Oscillation Theory for Sturm-Liouville Operators Extended

Details Relative Oscillation Theory for Sturm-Liouville Operators Extended Relative Oscillation Theory for Sturm-Liouville Operators Extended

2007-07-24

arxiv.org/abs/0707.3451v2

J. Funct. Anal. 254-6, 1702-1720 (2008)

Mathematics

Spectral Theory

16 pages

Scientific paper

10.1016/j.jfa.2007.10.007

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.

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