arXiv subjects

Helge Krueger

Publications and source records attributed to Helge Krueger.

21 records · Page 2Linked to original sources

arXiv2007

Effective Pruefer Angles and Relative Oscillation Criteria

We present a streamlined approach to relative oscillation criteria based on effective Pruefer angles adapted to the use at the edges of the essential spectrum. Based on this we provided a new scale of oscillation criteria for general Sturm-Liouville operators which answer the question whether a perturbation inserts a finite or an infinite number of eigenvalues into an essential spectral gap. As a special case we recover the Gesztesy-Uenal criterion (which works below the spectrum and contains classical criteria by Kneser, Hartman, Hille, and Weber) and the well-known results by Rofe-Beketov including the extensions by Schmidt.

math.SP↗

arXiv2007

On Perturbations of Quasiperiodic Schroedinger Operators

Using relative oscillation theory and the reducibility result of Eliasson, we study perturbations of quasiperiodic Schroedinger operators. In particular, we derive relative oscillation criteria and eigenvalue asymptotics for critical potentials.

math.SP↗

arXiv2007

Relative Oscillation Theory for Sturm-Liouville Operators Extended

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.

math.SP↗