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@article{692385,
author = {Hilscher, Roman and Růžičková, Viera},
article_location = {San Diego (USA)},
article_number = {2},
keywords = {Discrete symplectic system; Quadratic functional; Nonnegativity; Positivity; Riccati inequality; Riccati equation; Conjoined basis; Sturmian theorem},
language = {eng},
issn = {0022-247X},
journal = {Journal of Mathematical Analysis and Applications},
title = {Riccati inequality and other results for discrete symplectic systems},
volume = {322},
year = {2006}
}
TY - JOUR
ID - 692385
AU - Hilscher, Roman - Růžičková, Viera
PY - 2006
TI - Riccati inequality and other results for discrete symplectic systems
JF - Journal of Mathematical Analysis and Applications
VL - 322
IS - 2
SP - 1083-1098
EP - 1083-1098
PB - Elsevier Science
SN - 0022247X
KW - Discrete symplectic system
KW - Quadratic functional
KW - Nonnegativity
KW - Positivity
KW - Riccati inequality
KW - Riccati equation
KW - Conjoined basis
KW - Sturmian theorem
N2 - In this paper we establish several new results regarding the positivity and nonnegativity of discrete quadratic functionals F associated with discrete symplectic systems. In particular, we derive (i) the Riccati inequality for the positivity of F with separated endpoints, (ii) a characterization of the nonnegativity of F for the case of general (jointly varying) endpoints, and (iii) several perturbation-type inequalities regarding the nonnegativity of F with zero endpoints. Some of these results are new even for the special case of discrete Hamiltonian systems.
ER -
HILSCHER, Roman and Viera RŮŽIČKOVÁ. Riccati inequality and other results for discrete symplectic systems. \textit{Journal of Mathematical Analysis and Applications}. San Diego (USA): Elsevier Science, 2006, vol.~322, No~2, p.~1083-1098. ISSN~0022-247X.
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