Relative oscillation theory for Sturm-Liouville operators extended (Q2426489)

The purpose of the paper is to extend relative oscillation theory for two different Sturm-Liouville operators \[ H_ju=r^{-1}(-(p_ju')'+q_ju)\quad (j=0,1). \] The authors have shown that the weighted number of zeros of Wronskians of certain solutions equals to the value of Krein's spectral shift function \(\xi(\lambda,H_1,H_0)\) inside essential spectral gaps. The method of proof is based on finding a continuous path connecting the operators \(H_0\) and \(H_1\) in the metric introduced by the trace norm of resolvent differences.