Relative Oscillation Theory for Jacobi Matrices

Abstract

We develop relative oscillation theory for Jacobi matrices which, rather than counting the number of eigenvalues of one single matrix, counts the difference between the number of eigenvalues of two different matrices. This is done by replacing nodes of solutions associated with one matrix by weighted nodes of Wronskians of solutions of two different matrices.

8 pages

References in corpus (3)

• Effective Pruefer Angles and Relative Oscillation Criteria
• 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 (5)

• Relative Oscillation Theory, Weighted Zeros of the Wronskian, and the Spectral Shift Function
• Spectral Theory as Influenced by Fritz Gesztesy
• Relative Oscillation Theory for Dirac Operators
• Renormalized Oscillation Theory for Symplectic Eigenvalue Problems with Nonlinear Dependence on the Spectral Parameter
• Relative Oscillation Theory for Jacobi Matrices Extended