The Discrete Prüfer Transformation
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.
M. Bohner and O. Došlý, "The Discrete Prüfer Transformation," Proceedings of the American Mathematical Society, American Mathematical Society, Jan 2001.
The definitive version is available at http://dx.doi.org/10.1090/S0002-9939-01-05833-6
Mathematics and Statistics
Keywords and Phrases
Prüfer transformation; Sturm-Liouville difference equations; Linear Hamiltonian difference systems; time scales; Symplectic systems
Article - Journal
© 2001 American Mathematical Society, All rights reserved.