New existence results for conjoined bases of singular linear Hamiltonian systems with given Sturmian properties
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F25%3A00144244" target="_blank" >RIV/00216224:14310/25:00144244 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0024379524004373" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0024379524004373</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.laa.2024.11.017" target="_blank" >10.1016/j.laa.2024.11.017</a>
Alternative languages
Result language
angličtina
Original language name
New existence results for conjoined bases of singular linear Hamiltonian systems with given Sturmian properties
Original language description
In this paper we derive new existence results for conjoined bases of singular linear Hamiltonian differential systems with given qualitative (Sturmian) properties. In particular, we examine the existence of conjoined bases with invertible upper block and with prescribed number of focal points at the endpoints of the considered unbounded interval. Such results are vital for the theory of Riccati differential equations and its applications in optimal control problems. As the main tools we use a new general characterization of conjoined bases belonging to a given equivalence class (genus) and the theory of comparative index of two Lagrangian planes. We also utilize extensively the methods of matrix analysis. The results are new even for identically normal linear Hamiltonian systems. The results are also new for linear Hamiltonian systems on a compact interval, where they provide additional equivalent conditions to the classical Reid roundabout theorem about disconjugacy.
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
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA23-05242S" target="_blank" >GA23-05242S: Oscillation theory on hybrid time domains with applications in spectral theory and matrix analysis</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2025
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
1873-1856
Volume of the periodical
707
Issue of the periodical within the volume
February
Country of publishing house
US - UNITED STATES
Number of pages
38
Pages from-to
187-224
UT code for WoS article
001406712200001
EID of the result in the Scopus database
2-s2.0-85210300880