Lidskii angles and Sturmian theory for linear Hamiltonian
systems on compact interval

J 2021

Lidskii angles and Sturmian theory for linear Hamiltonian systems on compact interval

ŠEPITKA, Peter a Roman ŠIMON HILSCHER

Základní údaje

Originální název

Lidskii angles and Sturmian theory for linear Hamiltonian systems on compact interval

Autoři

ŠEPITKA, Peter (703 Slovensko, domácí) a Roman ŠIMON HILSCHER (203 Česká republika, garant, domácí)

Vydání

Journal of Differential Equations, Elsevier, 2021, 0022-0396

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Spojené státy

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 2.615

Kód RIV

RIV/00216224:14310/21:00119050

Organizační jednotka

Přírodovědecká fakulta

DOI

http://dx.doi.org/10.1016/j.jde.2021.06.037

UT WoS

000681321100001

EID Scopus

2-s2.0-85109165913

Klíčová slova anglicky

Linear Hamiltonian system; Lidskii angle; Focal point; Principal solution; Sturmian separation theorem; Limit theorem

Štítky

rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 2. 9. 2021 14:20, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

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.

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. Lidskii angles and Sturmian theory for linear Hamiltonian systems on compact interval. Journal of Differential Equations. Elsevier, 2021, roč. 298, October, s. 1-29. ISSN 0022-0396. Dostupné z: https://dx.doi.org/10.1016/j.jde.2021.06.037.

@article{1781698,
   author = {Šepitka, Peter and Šimon Hilscher, Roman},
   article_number = {October},
   doi = {http://dx.doi.org/10.1016/j.jde.2021.06.037},
   keywords = {Linear Hamiltonian system; Lidskii angle; Focal point; Principal solution; Sturmian separation theorem; Limit theorem},
   language = {eng},
   issn = {0022-0396},
   journal = {Journal of Differential Equations},
   title = {Lidskii angles and Sturmian theory for linear Hamiltonian systems on compact interval},
   url = {https://doi.org/10.1016/j.jde.2021.06.037},
   volume = {298},
   year = {2021}
}

TY  - JOUR
ID  - 1781698
AU  - Šepitka, Peter - Šimon Hilscher, Roman
PY  - 2021
TI  - Lidskii angles and Sturmian theory for linear Hamiltonian systems on compact interval
JF  - Journal of Differential Equations
VL  - 298
IS  - October
SP  - 1-29
EP  - 1-29
PB  - Elsevier
SN  - 00220396
KW  - Linear Hamiltonian system
KW  - Lidskii angle
KW  - Focal point
KW  - Principal solution
KW  - Sturmian separation theorem
KW  - Limit theorem
UR  - https://doi.org/10.1016/j.jde.2021.06.037
N2  - 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.
ER  -

ŠEPITKA, Peter a Roman ŠIMON HILSCHER. Lidskii angles and Sturmian theory for linear Hamiltonian systems on compact interval. \textit{Journal of Differential Equations}. Elsevier, 2021, roč.~298, October, s.~1-29. ISSN~0022-0396. Dostupné z: https://dx.doi.org/10.1016/j.jde.2021.06.037.

Přehled o publikaci