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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The discrete Prüfer transformation


Authors: Martin Bohner and Ondrej Doslý
Journal: Proc. Amer. Math. Soc. 129 (2001), 2715-2726
MSC (2000): Primary 39A12; Secondary 39A11, 34K11
Published electronically: February 15, 2001
MathSciNet review: 1838796
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Abstract:

The classical Prüfer transformation has proved to be a useful tool in the study of Sturm-Liouville theory. In this paper we introduce the Prüfer transformation for self-adjoint difference equations and use it to obtain oscillation criteria and other results. We then offer an extension of this approach to the case of general symplectic systems on time scales. Time scales have been introduced in order to unify discrete and continuous analysis, and indeed our results cover as special cases both the Prüfer transformation for differential and for difference equations.


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Additional Information

Martin Bohner
Affiliation: Department of Mathematics and Statistics, University of Missouri–Rolla, 313 Rolla Building, Rolla, Missouri 65409-0020
Email: bohner@umr.edu

Ondrej Doslý
Affiliation: Mathematical Institute, Czech Academy of Sciences, Žižkova 22, CZ–61662 Brno, Czech Republic
Email: dosly@math.muni.cz

DOI: http://dx.doi.org/10.1090/S0002-9939-01-05833-6
PII: S 0002-9939(01)05833-6
Keywords: Pr\"ufer transformation, Sturm-Liouville difference equations, linear Hamiltonian difference systems, time scales, symplectic systems
Received by editor(s): September 2, 1999
Received by editor(s) in revised form: January 24, 2000
Published electronically: February 15, 2001
Additional Notes: The research of the first author was supported by the University of Missouri Research Board. The research of the second author was supported by the Grant G201/98/0677 of the Czech Grant Agency (Prague).
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2001 American Mathematical Society