Space versus energy oscillations of Prufer phases for matrix Sturm-Liouville and Jacobi operators
Date
2020-07-17
Authors
Schulz-Baldes, Hermann
Urban, Liam
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
This note considers Sturm oscillation theory for regular matrix Sturm-Liouville operators on finite intervals and for matrix Jacobi operators. The number of space oscillations of the eigenvalues of the matrix Prüfer phases at a given energy, defined by a suitable lift in the Jacobi case, is shown to be equal to the number of eigenvalues below that energy. This results from a positivity property of the Prüfer phases, namely they cannot cross -1 in the negative direction, and is also shown to be closely linked to the positivity of the matrix Prüfer phase in the energy variable. The theory is illustrated by numerical calculations for an explicit example.
Description
Keywords
Sturm-Liouville operators, Jacobi operators, Oscillation Theory, Matrix Prüfer phases
Citation
Schulz-Baldes, H., & Urban, L. (2020). Space versus energy oscillations of Prufer phases for matrix Sturm-Liouville and Jacobi operators. <i>Electronic Journal of Differential Equations, 2020</i>(76), pp. 1-23.
Rights
Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.