The Discrete Prüfer Transformation

Author

Martin Bohner, Missouri University of Science and TechnologyFollow
Ondřej Došlý

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.

Recommended Citation

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 https://doi.org/10.1090/S0002-9939-01-05833-6

Department(s)

Mathematics and Statistics

Keywords and Phrases

Prüfer transformation; Sturm-Liouville difference equations; Linear Hamiltonian difference systems; time scales; Symplectic systems

International Standard Serial Number (ISSN)

0002-9939

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2001 American Mathematical Society, All rights reserved.

Publication Date

01 Jan 2001