Helge Krüger, Gerald Teschl
Relative Oscillation Theory for Sturm-Liouville Operators Extended
The paper is published:
J. Funct. Anal. 254-6 (2008) 1702-1720
- MSC:
- 34B24 Sturm-Liouville theory, See also {34Lxx}
- 34C10 Oscillation theory, zeros, disconjugacy and comparison theory
- 34L15 Estimation of eigenvalues, upper and lower bounds
- 34L05 General spectral theory
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.
Keywords: Sturm--Liouville operators, oscillation theory, spectral shift function
Notes: second and final version