Limit circle invariance for two differential systems on time scales

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F15%3A00080585" target="_blank" >RIV/00216224:14310/15:00080585 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1002/mana.201400005" target="_blank" >http://dx.doi.org/10.1002/mana.201400005</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/mana.201400005" target="_blank" >10.1002/mana.201400005</a>

Result language
angličtina
Original language name
Limit circle invariance for two differential systems on time scales
Original language description
In this paper we consider two linear differential systems on a time scale. Both systems depend linearly on a complex spectral parameter lambda. We prove that if all solutions of these two systems are square integrable with respect to a given weight matrix for one value lambda, then this property is preserved for all complex values lambda. This result extends and improves the corresponding continuous time statement, which was derived by Walker (1975) for two non-hermitian linear Hamiltonian systems, to appropriate differential systems on arbitrary time scales. The result is new even in the purely discrete case, or in the scalar time scale case, as well as when both time scale systems coincide. The latter case also generalizes a limit circle invariance criterion for symplectic systems on time scales, which was recently derived by the authors.
Czech name
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Czech description
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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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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)

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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