Linear Hamiltonian systems on time scales: positivity of quadratic functionals
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F00%3A00008156" target="_blank" >RIV/00216224:14310/00:00008156 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
Linear Hamiltonian systems on time scales: positivity of quadratic functionals
Original language description
In this work we consider a linear Hamiltonian system (H) <p> <center> x<sup>Delta</sup> = A<sub>t</sub> x<sup>sigma</sup> + B<sub>t</sub> u, <br> u<sup>Delta</sup> = -C<sub>t</sub> x<sup>sigma</sup> - A<sub>t</sub><sup>T</sup> u </center> </p> <p> onan arbitrary time scale T, which allows (among others) <ul> <li> to treat both continuous and discrete linear Hamiltonian systems (as the special cases for T=R and T=Z) within one theory; </li> <li> to explain the discrepancies between these two theories while studying systems of the form (H). </li> </ul> As a main result we prove that disconjugacy of the system (H) is a sufficient condition for positive definiteness of the quadratic functional associated with (H). The principal tool is the Picone identity on T. We derive also the corresponding Wronskian identity, Riccati equation in this general setting on time scales.</p>
Czech name
Linear Hamiltonian systems on time scales: positivity of quadratic functionals
Czech description
In this work we consider a linear Hamiltonian system (H) <p> <center> x<sup>Delta</sup> = A<sub>t</sub> x<sup>sigma</sup> + B<sub>t</sub> u, <br> u<sup>Delta</sup> = -C<sub>t</sub> x<sup>sigma</sup> - A<sub>t</sub><sup>T</sup> u </center> </p> <p> onan arbitrary time scale T, which allows (among others) <ul> <li> to treat both continuous and discrete linear Hamiltonian systems (as the special cases for T=R and T=Z) within one theory; </li> <li> to explain the discrepancies between these two theories while studying systems of the form (H). </li> </ul> As a main result we prove that disconjugacy of the system (H) is a sufficient condition for positive definiteness of the quadratic functional associated with (H). The principal tool is the Picone identity on T. We derive also the corresponding Wronskian identity, Riccati equation in this general setting on time scales.</p>
Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2000
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematical and Computer Modelling
ISSN
0895-7177
e-ISSN
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Volume of the periodical
32
Issue of the periodical within the volume
5-6
Country of publishing house
US - UNITED STATES
Number of pages
20
Pages from-to
507-527
UT code for WoS article
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EID of the result in the Scopus database
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