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@article{695806,
author = {Hilscher, Roman and Zeidan, Vera},
article_location = {San Diego (USA)},
article_number = {1},
keywords = {Time scale; Time scale symplectic system; Linear Hamiltonian system; Quadratic functional; Nonnegativity; Positivity; Conjoined basis; Generalized focal point},
language = {eng},
issn = {0022-0396},
journal = {Journal of Differential Equations},
title = {Time scale symplectic systems without normality},
volume = {230},
year = {2006}
}
TY - JOUR
ID - 695806
AU - Hilscher, Roman - Zeidan, Vera
PY - 2006
TI - Time scale symplectic systems without normality
JF - Journal of Differential Equations
VL - 230
IS - 1
SP - 140-173
EP - 140-173
PB - Elsevier Science
SN - 00220396
KW - Time scale
KW - Time scale symplectic system
KW - Linear Hamiltonian system
KW - Quadratic functional
KW - Nonnegativity
KW - Positivity
KW - Conjoined basis
KW - Generalized focal point
N2 - We present a theory of the definiteness (nonnegativity and positivity) of a quadratic functional F over a bounded time scale. The results are given in terms of a time scale symplectic system (S), which is a time scale linear system that generalizes and unifies the linear Hamiltonian differential system and discrete symplectic system. The novelty of this paper resides in removing the assumption of normality in the characterization of the positivity of F, and in establishing equivalent conditions for the nonnegativity of F without any normality assumption. To reach this goal, a new notion of generalized focal points for conjoined bases (X,U) of (S) is introduced, results on the piecewise-constant kernel of X(t) are obtained, and various Picone-type identities are derived under the piecewise-constant kernel condition.
ER -
HILSCHER, Roman a Vera ZEIDAN. Time scale symplectic systems without normality. Online. \textit{Journal of Differential Equations}. San Diego (USA): Elsevier Science, 2006, roč.~230, č.~1, s.~140-173. ISSN~0022-0396. [citováno 2024-04-23]
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