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@article{488380,
author = {Hilscher, Roman},
article_location = {Berlin},
article_number = {1},
keywords = {time scale; (continuous and discrete) linear Hamiltonian system; quadratic functional; disconjugacy; focal point; principal solution},
language = {eng},
issn = {0025-584X},
journal = {Mathematische Nachrichten},
title = {Positivity of quadratic functionals on time scales: necessity},
volume = {226},
year = {2001}
}
TY - JOUR
ID - 488380
AU - Hilscher, Roman
PY - 2001
TI - Positivity of quadratic functionals on time scales: necessity
JF - Mathematische Nachrichten
VL - 226
IS - 1
SP - 85-98
EP - 85-98
PB - WILEY-VCH Verlag
SN - 0025584X
KW - time scale
KW - (continuous and discrete) linear Hamiltonian system
KW - quadratic functional
KW - disconjugacy
KW - focal point
KW - principal solution
N2 - In this work we establish that disconjugacy of a linear Hamiltonian system on time scales is a necessary condition for the positivity of the corresponding quadratic functional. We employ a certain minimal normality (controllability) assumption. Hence, the open problems stated by the author in [15], [16] are solved with the result that positivity of the quadratic functional is equivalent with disconjugacy of the Hamiltonian system on the interval under consideration. The general approach on time scales T involves, as special cases, the well known continuous case for T=R and recently developed discrete one for T=Z, so that they are unified. As applications, Sturmian type separation and comparison theorems on time scales are also provided.
ER -
HILSCHER, Roman. Positivity of quadratic functionals on time scales: necessity. \textit{Mathematische Nachrichten}. Berlin: WILEY-VCH Verlag, 2001, vol.~226, No~1, p.~85-98. ISSN~0025-584X.
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