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Positivity of Quadratic Functionals on Time Scales: Necessity

✍ Scribed by Roman Hilscher

Publisher
John Wiley and Sons
Year
2001
Tongue
English
Weight
198 KB
Volume
226
Category
Article
ISSN
0025-584X

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✦ Synopsis

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 [17], [18] are solved with the result that positivity of the quadratic functional is equivalent to 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 = IR and recently developed discrete one for T = Z Z, so that they are unified. As applications, Sturmian type separation and comparison theorems on time scales are also provided.

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