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@article{842151, author = {Šimon Hilscher, Roman and Zemánek, Petr}, article_location = {Delhi (Indie)}, article_number = {1}, keywords = {Linear Hamiltonian system; Discrete symplectic system; Time scale; Time scale symplectic system; Quadratic functional; Conjoined basis; Focal point; Nonnegativity; Positivity}, language = {eng}, issn = {0973-6069}, journal = {International Journal of Difference Equations}, title = {Definiteness of quadratic functionals for Hamiltonian and symplectic systems: A survey}, volume = {4}, year = {2009} }
TY - JOUR ID - 842151 AU - Šimon Hilscher, Roman - Zemánek, Petr PY - 2009 TI - Definiteness of quadratic functionals for Hamiltonian and symplectic systems: A survey JF - International Journal of Difference Equations VL - 4 IS - 1 SP - 49-67 EP - 49-67 PB - Research India Publications SN - 09736069 KW - Linear Hamiltonian system KW - Discrete symplectic system KW - Time scale KW - Time scale symplectic system KW - Quadratic functional KW - Conjoined basis KW - Focal point KW - Nonnegativity KW - Positivity N2 - In this paper we provide a survey of characterizations of the nonnegativity and positivity of quadratic functionals arising in the theory of linear Hamiltonian and symplectic systems. We study these functionals on traditional continuous time domain (under and without controllability), on discrete domain, and on time scale domain which unifies and extends both previous types. For each case we distinguish functionals with zero, separated, and jointly varying endpoints. The presented conditions are formulated in terms of the properties of a special conjoined basis of the considered linear system. It is now easy to compare all the results - between continuous, discrete, and time scale cases, between the zero, separated, and jointly varying endpoits, and between the nonnegativity and positivity. ER -
ŠIMON HILSCHER, Roman a Petr ZEMÁNEK. Definiteness of quadratic functionals for Hamiltonian and symplectic systems: A survey. \textit{International Journal of Difference Equations}. Delhi (Indie): Research India Publications, 2009, roč.~4, č.~1, s.~49-67. ISSN~0973-6069.
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