Effective Pruefer Angles and Relative Oscillation Criteria

Abstract

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.

22 pages

References in corpus (2)

• Relative Oscillation Theory, Weighted Zeros of the Wronskian, and the Spectral Shift Function
• Relative Oscillation Theory for Sturm-Liouville Operators Extended

Cited by in corpus (9)

• Relative Oscillation Theory, Weighted Zeros of the Wronskian, and the Spectral Shift Function
• Relative Oscillation Theory for Jacobi Matrices
• Spectral Theory as Influenced by Fritz Gesztesy
• Relative Oscillation Theory for Dirac Operators
• Trace Formulas for Schroedinger Operators in Connection with Scattering Theory for Finite-Gap Backgrounds
• Scattering theory for Schrödinger operators on steplike, almost periodic infinite-gap backgrounds
• On Perturbations of Quasiperiodic Schroedinger Operators
• Relative oscillation theory and essential spectra of Sturm--Liouville operators
• The Transformation Operator for One-Dimensional Schroedinger Operators on Almost Periodic Infinite-Gap Backgrounds