Space versus energy oscillations of Prufer phases for matrix Sturm-Liouville and Jacobi operators

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dc.contributor.authorSchulz-Baldes, Hermann
dc.contributor.authorUrban, Liam
dc.date.accessioned2021-10-04T13:20:39Z
dc.date.available2021-10-04T13:20:39Z
dc.date.issued2020-07-17
dc.description.abstractThis 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.
dc.description.departmentMathematics
dc.formatText
dc.format.extent23 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationSchulz-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.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/14584
dc.language.isoen
dc.publisherTexas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.holderThis work is licensed under a Creative Commons Attribution 4.0 International License.
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2020, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectSturm-Liouville operators
dc.subjectJacobi operators
dc.subjectOscillation Theory
dc.subjectMatrix Prüfer phases
dc.titleSpace versus energy oscillations of Prufer phases for matrix Sturm-Liouville and Jacobi operators
dc.typeArticle

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