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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The discrete Prüfer transformation
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by Martin Bohner and Ondřej Došlý PDF
Proc. Amer. Math. Soc. 129 (2001), 2715-2726 Request permission

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
  • MR Author ID: 295863
  • ORCID: 0000-0001-8310-0266
  • Email: bohner@umr.edu
  • Ondřej Došlý
  • Affiliation: Mathematical Institute, Czech Academy of Sciences, Žižkova 22, CZ–61662 Brno, Czech Republic
  • Email: dosly@math.muni.cz
  • 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
  • © Copyright 2001 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 129 (2001), 2715-2726
  • MSC (2000): Primary 39A12; Secondary 39A11, 34K11
  • DOI: https://doi.org/10.1090/S0002-9939-01-05833-6
  • MathSciNet review: 1838796