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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA19-01246S" target="_blank" >GA19-01246S: Nová oscilační teorie pro lineární hamiltonovské a symplektické systémy</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Differential Equations

ISSN

0022-0396

e-ISSN

1090-2732

Svazek periodika

298

Číslo periodika v rámci svazku

October

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

29

Strana od-do

1-29

Kód UT WoS článku

000681321100001

EID výsledku v databázi Scopus

2-s2.0-85109165913