Positive Semidefiniteness of Discrete Quadratic Functionals
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.
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 http://dx.doi.org/10.1017/S0013091502001086
Mathematics and Statistics
Keywords and Phrases
Hamiltonian systems; symplectic systems; discrete quadratic functionals; non-negativity
Article - Conference proceedings
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