Positive Semidefiniteness of Discrete Quadratic Functionals

Author

Martin Bohner, Missouri University of Science and TechnologyFollow
Ondřej Došlý
Werner Kratz

Abstract

We consider symplectic difference systems, which contain as special cases linear Hamiltonian difference systems and Sturm–Liouville difference equations of any even order. An associated discrete quadratic functional is important in discrete variational analysis, and while its positive definiteness has been characterized and is well understood, a characterization of its positive semidefiniteness remained an open problem. In this paper we present the solution to this problem and offer necessary and sufficient conditions for such discrete quadratic functionals to be non-negative definite.

Recommended Citation

M. Bohner et al., "Positive Semidefiniteness of Discrete Quadratic Functionals," Proceedings of the Edinburgh Mathematical Society, Cambridge University Press, Jan 2003.

The definitive version is available at https://doi.org/10.1017/S0013091502001086

Department(s)

Mathematics and Statistics

Keywords and Phrases

Hamiltonian systems; symplectic systems; discrete quadratic functionals; non-negativity

Document Type

Article - Conference proceedings

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2003 Cambridge University Press, All rights reserved.

Publication Date

01 Jan 2003