Monotonicity and limit results for certain symmetric matrix-valued functions with applications in singular Sturmian theory

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F25%3A00144318" target="_blank" >RIV/00216224:14310/25:00144318 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1080/27690911.2025.2494577" target="_blank" >https://doi.org/10.1080/27690911.2025.2494577</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1080/27690911.2025.2494577" target="_blank" >10.1080/27690911.2025.2494577</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Monotonicity and limit results for certain symmetric matrix-valued functions with applications in singular Sturmian theory

Popis výsledku v původním jazyce

In this paper we study the monotonicity and limit properties at infinity of certain symmetric matrix-valued functions arising in the singular Sturmian theory of canonical linear differential systems. We develop a new method for studying such matrices on an unbounded interval, where we employ the limit properties of Wronskians with the minimal principal solution at infinity to represent the value of the given symmetric matrix at infinity. Moreover, we use the Moore-Penrose pseudoinverse matrices to consider possibly noninvertible solutions of the system. We apply this knowledge for deriving singular Sturmian-type separation theorems on unbounded intervals, which are formulated in terms of the limit properties of the Lidskii angles of the symplectic fundamental matrix of the system. In this way we also extend to the unbounded intervals our results on this subject [Šepitka P, Šimon Hilscher R. Lidskii angles and Sturmian theory for linear Hamiltonian systems on compact interval. J Differ Equ. 2021;298:1-29. doi: 10.1016/j.jde.2021.06.037] regarding the Sturmian separation theorems on a compact interval.

Název v anglickém jazyce

Monotonicity and limit results for certain symmetric matrix-valued functions with applications in singular Sturmian theory

Popis výsledku anglicky

In this paper we study the monotonicity and limit properties at infinity of certain symmetric matrix-valued functions arising in the singular Sturmian theory of canonical linear differential systems. We develop a new method for studying such matrices on an unbounded interval, where we employ the limit properties of Wronskians with the minimal principal solution at infinity to represent the value of the given symmetric matrix at infinity. Moreover, we use the Moore-Penrose pseudoinverse matrices to consider possibly noninvertible solutions of the system. We apply this knowledge for deriving singular Sturmian-type separation theorems on unbounded intervals, which are formulated in terms of the limit properties of the Lidskii angles of the symplectic fundamental matrix of the system. In this way we also extend to the unbounded intervals our results on this subject [Šepitka P, Šimon Hilscher R. Lidskii angles and Sturmian theory for linear Hamiltonian systems on compact interval. J Differ Equ. 2021;298:1-29. doi: 10.1016/j.jde.2021.06.037] regarding the Sturmian separation theorems on a compact interval.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA23-05242S" target="_blank" >GA23-05242S: Oscilační teorie na hybridních časových doménách s aplikacemi ve spektrální teorii a maticové analýze</a><br>

Návaznosti

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

Rok uplatnění

2025

Kód důvěrnosti údajů

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

Název periodika

Applied Mathematics in Science and Engineering

ISSN

2769-0911

e-ISSN

2769-0911

Svazek periodika

33

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

39

Strana od-do

1-39

Kód UT WoS článku

001484872600001

EID výsledku v databázi Scopus

2-s2.0-105004794444