Relative Oscillation Theory for Sturm-Liouville Operators Extended

Abstract

We extend relative oscillation theory to the case of Sturm--Liouville operators $Hu=r^{-1}(-(p{u}^{\prime }{)}^{\prime }+qu)$ 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

References in corpus (1)

• Relative Oscillation Theory, Weighted Zeros of the Wronskian, and the Spectral Shift Function

Cited by in corpus (8)

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• Relative Oscillation Theory for Jacobi Matrices Extended