POSITIVE SEMIDEFINITENESS OF DISCRETE QUADRATIC FUNCTIONALS

Martin Bohner, Ondřej Došlý, Werner Kratz
2003 Proceedings of the Edinburgh Mathematical Society  
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
more » ... d offer necessary and sufficient conditions for such discrete quadratic functionals to be non-negative definite.
doi:10.1017/s0013091502001086 fatcat:ol7p3hwk4zbibaagqqyfuki4iu