Distribution and number of focal points for linear Hamiltonian systems
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F21%3A00118790" target="_blank" >RIV/00216224:14310/21:00118790 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.laa.2020.11.018" target="_blank" >https://doi.org/10.1016/j.laa.2020.11.018</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.laa.2020.11.018" target="_blank" >10.1016/j.laa.2020.11.018</a>
Alternative languages
Result language
angličtina
Original language name
Distribution and number of focal points for linear Hamiltonian systems
Original language description
In this paper we consider the question of distribution and number of left and right focal points for conjoined bases of linear Hamiltonian differential systems. We do not assume any complete controllability (identical normality) condition. Recently we obtained the Sturmian separation theorem for this case which provides optimal lower and upper bounds for the numbers of left and right focal points of every conjoined basis in terms of the principal solutions at the endpoints of the interval. In this paper we show that for any two given integers within these bounds there exists a conjoined basis with these prescribed numbers of left and right focal points. We determine such conjoined bases by their initial conditions. Our approach is to transfer the problem through the comparative index into matrix analysis. The main results are new even for completely controllable linear Hamiltonian systems. As an application we extend a classical result for controllable systems by Reid (1971) about the existence of conjoined bases with an invertible first component.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA19-01246S" target="_blank" >GA19-01246S: New oscillation theory for linear Hamiltonian and symplectic systems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Linear Algebra and Its Applications
ISSN
0024-3795
e-ISSN
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Volume of the periodical
611
Issue of the periodical within the volume
February 2021
Country of publishing house
US - UNITED STATES
Number of pages
20
Pages from-to
26-45
UT code for WoS article
000600065400002
EID of the result in the Scopus database
2-s2.0-85097336569