Weak disconjugacy, weak controllability, and genera of
conjoined bases for linear Hamiltonian systems

J 2022

Weak disconjugacy, weak controllability, and genera of conjoined bases for linear Hamiltonian systems

ŠEPITKA, Peter a Roman ŠIMON HILSCHER

Základní údaje

Originální název

Weak disconjugacy, weak controllability, and genera of conjoined bases for linear Hamiltonian systems

Autoři

ŠEPITKA, Peter a Roman ŠIMON HILSCHER

Vydání

Annali di Matematica Pura ed Applicata, Springer, 2022, 0373-3114

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Německo

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 1.000

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/22:00129036

Organizační jednotka

Přírodovědecká fakulta

Klíčová slova anglicky

Linear Hamiltonian system; Weak disconjugacy; Weak controllability; Genus of conjoined bases; Nonoscillation; Maximal order of abnormality; Principal solution at infinity

Štítky

14311010, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 17. 10. 2022 08:12, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

In this paper, we discuss mutual interrelations between the notions of weak disconjugacy and weak controllability for linear Hamiltonian differential systems. These notions have been used in connection with the study of exponential dichotomy, nonoscillation, and dissipative control processes for these systems [e.g. (Johnson et al., in: Nonautonomous linear Hamiltonian systems: oscillation, spectral theory and control developments in mathematics, Springer, Cham, 2016)]. As our main results, we derive characterizations of the weak controllability and weak disconjugacy in terms of properties of certain subspaces arising in the recently introduced theory of genera of conjoined bases for linear Hamiltonian systems (Sepitka in J Dyn Differ Equ 32(3):1139-1155, 2020). We also present new results regarding the zero value of the maximal order of abnormality of the system in terms of a weak controllability condition, or in terms of a weak disconjugacy condition when the system is nonoscillatory and satisfies the Legendre condition. In our accompanying comments, we highlight the connections of the theory of genera of conjoined bases with the existence of principal solutions at infinity, which arise in the study of weakly disconjugate linear Hamiltonian systems. The results in this paper may be regarded as a completion and clarification of the previous considerations in the literature about the weak disconjugacy and weak controllability conditions for linear Hamiltonian systems [e.g. (Fabbri et al. in: J Math Anal Appl 380(2):853-864, 2011), (Johnson et al., in Nonautonomous linear Hamiltonian systems: oscillation, spectral theory and control developments in mathematics, Springer, Cham, 2016)].

Návaznosti

GA19-01246S, projekt VaV

Název: Nová oscilační teorie pro lineární hamiltonovské a symplektické systémy

Investor: Grantová agentura ČR, Nová oscilační teorie pro lineární hamiltonovské a symplektické systémy

Citovat

ŠEPITKA, Peter a Roman ŠIMON HILSCHER. Weak disconjugacy, weak controllability, and genera of conjoined bases for linear Hamiltonian systems. Annali di Matematica Pura ed Applicata. Springer, 2022, roč. 201, č. 5, s. 2121-2136. ISSN 0373-3114. Dostupné z: https://doi.org/10.1007/s10231-022-01194-x.

@article{1840397,
   author = {Šepitka, Peter and Šimon Hilscher, Roman},
   article_number = {5},
   doi = {https://doi.org/10.1007/s10231-022-01194-x},
   keywords = {Linear Hamiltonian system; Weak disconjugacy; Weak controllability; Genus of conjoined bases; Nonoscillation; Maximal order of abnormality; Principal solution at infinity},
   language = {eng},
   issn = {0373-3114},
   journal = {Annali di Matematica Pura ed Applicata},
   title = {Weak disconjugacy, weak controllability, and genera of conjoined bases for linear Hamiltonian systems},
   url = {https://link.springer.com/article/10.1007/s10231-022-01194-x},
   volume = {201},
   year = {2022}
}

TY  - JOUR
ID  - 1840397
AU  - Šepitka, Peter - Šimon Hilscher, Roman
PY  - 2022
TI  - Weak disconjugacy, weak controllability, and genera of conjoined bases for linear Hamiltonian systems
JF  - Annali di Matematica Pura ed Applicata
VL  - 201
IS  - 5
SP  - 2121-2136
EP  - 2121-2136
PB  - Springer
SN  - 03733114
KW  - Linear Hamiltonian system
KW  - Weak disconjugacy
KW  - Weak controllability
KW  - Genus of conjoined bases
KW  - Nonoscillation
KW  - Maximal order of abnormality
KW  - Principal solution at infinity
UR  - https://link.springer.com/article/10.1007/s10231-022-01194-x
N2  - In this paper, we discuss mutual interrelations between the notions of weak disconjugacy and weak controllability for linear Hamiltonian differential systems. These notions have been used in connection with the study of exponential dichotomy, nonoscillation, and dissipative control processes for these systems [e.g. (Johnson et al., in: Nonautonomous linear Hamiltonian systems: oscillation, spectral theory and control developments in mathematics, Springer, Cham, 2016)]. As our main results, we derive characterizations of the weak controllability and weak disconjugacy in terms of properties of certain subspaces arising in the recently introduced theory of genera of conjoined bases for linear Hamiltonian systems (Sepitka in J Dyn Differ Equ 32(3):1139-1155, 2020). We also present new results regarding the zero value of the maximal order of abnormality of the system in terms of a weak controllability condition, or in terms of a weak disconjugacy condition when the system is nonoscillatory and satisfies the Legendre condition. In our accompanying comments, we highlight the connections of the theory of genera of conjoined bases with the existence of principal solutions at infinity, which arise in the study of weakly disconjugate linear Hamiltonian systems. The results in this paper may be regarded as a completion and clarification of the previous considerations in the literature about the weak disconjugacy and weak controllability conditions for linear Hamiltonian systems [e.g. (Fabbri et al. in: J Math Anal Appl 380(2):853-864, 2011), (Johnson et al., in Nonautonomous linear Hamiltonian systems: oscillation, spectral theory and control developments in mathematics, Springer, Cham, 2016)].
ER  -

ŠEPITKA, Peter a Roman ŠIMON HILSCHER. Weak disconjugacy, weak controllability, and genera of conjoined bases for linear Hamiltonian systems. \textit{Annali di Matematica Pura ed Applicata}. Springer, 2022, roč.~201, č.~5, s.~2121-2136. ISSN~0373-3114. Dostupné z: https://doi.org/10.1007/s10231-022-01194-x.

Přehled o publikaci