R.Hilscher, V.Zeidan

Nabla time scale symplectic systems and related quadratic functionals

Abstract

In this paper we present the theory of nabla time scale symplectic systems. In particular, we establish conditions characterizing the positivity and nonnegativity of the quadratic functionals associated with such systems. These results are parallel (or dual) to the ones obtained recently by the authors for the delta time scale symplectic systems without normality assumption. A surprising outcome of this theory is the fact that some of the known results for the delta time scale case and the presented new results for the nabla time scale case do not coincide in the special cases of both continuous linear Hamiltonian systems and discrete symplectic systems. To the contrary, the nabla time scale results are also new in the latter two special cases. As applications of the obtained positivity and nonnegativity results we derive the Reid roundabout theorems for nabla time scale symplectic systems.



Zpatky na publikace. / Back to publications.
Zpatky na hlavni stranu. / Back to the main page.

Last change: September 4, 2008. (c) Roman Hilscher