Lidskii angles and Sturmian theory for linear Hamiltonian systems on compact interval
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F21%3A00119050" target="_blank" >RIV/00216224:14310/21:00119050 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.jde.2021.06.037" target="_blank" >https://doi.org/10.1016/j.jde.2021.06.037</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jde.2021.06.037" target="_blank" >10.1016/j.jde.2021.06.037</a>
Alternative languages
Result language
angličtina
Original language name
Lidskii angles and Sturmian theory for linear Hamiltonian systems on compact interval
Original language description
In this paper we investigate the Sturmian theory for general (possibly uncontrollable) linear Hamiltonian systems by means of the Lidskii angles, which are associated with a symplectic fundamental matrix of the system. In particular, under the Legendre condition we derive formulas for the multiplicities of the left and right proper focal points of a conjoined basis of the system, as well as the Sturmian separation theorems for two conjoined bases of the system, in terms of the Lidskii angles. The results are new even in the completely controllable case. As the main tool we use the limit theorem for monotone matrix-valued functions by Kratz (1993). The methods allow to present a new proof of the known monotonicity property of the Lidskii angles. The results and methods can also be potentially applied in the singular Sturmian theory on unbounded intervals, in the oscillation theory of linear Hamiltonian systems without the Legendre condition, in the comparative index theory, or in linear algebra in the theory of matrices.
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
Journal of Differential Equations
ISSN
0022-0396
e-ISSN
1090-2732
Volume of the periodical
298
Issue of the periodical within the volume
October
Country of publishing house
US - UNITED STATES
Number of pages
29
Pages from-to
1-29
UT code for WoS article
000681321100001
EID of the result in the Scopus database
2-s2.0-85109165913