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

J 2025

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

ŠEPITKA, Peter a Roman ŠIMON HILSCHER

Základní údaje

Originální název

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

Autoři

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

Vydání

Applied Mathematics in Science and Engineering, Taylor & Francis Ltd, 2025, 2769-0911

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Velká Británie a Severní Irsko

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 1.900 v roce 2023

Organizační jednotka

Přírodovědecká fakulta

DOI

http://dx.doi.org/10.1080/27690911.2025.2494577

UT WoS

001484872600001

EID Scopus

2-s2.0-105004794444

Klíčová slova anglicky

Symmetric matrix-valued function; limit theorem; Moore–Penrose pseudoinverse; linear hamiltonian system; Sturmian theory; Wronskian; Lidskii angles; principal solution at infinity

Štítky

rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 22. 5. 2025 09:20, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

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.

Návaznosti

GA23-05242S, projekt VaV

Název: Oscilační teorie na hybridních časových doménách s aplikacemi ve spektrální teorii a maticové analýze

Investor: Grantová agentura ČR, Oscilační teorie na hybridních časových doménách s aplikacemi ve spektrální a maticové analýze

Citovat

ŠEPITKA, Peter a Roman ŠIMON HILSCHER. Monotonicity and limit results for certain symmetric matrix-valued functions with applications in singular Sturmian theory. Applied Mathematics in Science and Engineering. Taylor & Francis Ltd, 2025, roč. 33, č. 1, s. 1-39. ISSN 2769-0911. Dostupné z: https://dx.doi.org/10.1080/27690911.2025.2494577.

@article{2496000,
   author = {Šepitka, Peter and Šimon Hilscher, Roman},
   article_number = {1},
   doi = {http://dx.doi.org/10.1080/27690911.2025.2494577},
   keywords = {Symmetric matrix-valued function; limit theorem; Moore–Penrose pseudoinverse; linear hamiltonian system; Sturmian theory; Wronskian; Lidskii angles; principal solution at infinity},
   language = {eng},
   issn = {2769-0911},
   journal = {Applied Mathematics in Science and Engineering},
   title = {Monotonicity and limit results for certain symmetric matrix-valued functions with applications in singular Sturmian theory},
   url = {https://doi.org/10.1080/27690911.2025.2494577},
   volume = {33},
   year = {2025}
}

TY  - JOUR
ID  - 2496000
AU  - Šepitka, Peter - Šimon Hilscher, Roman
PY  - 2025
TI  - Monotonicity and limit results for certain symmetric matrix-valued functions with applications in singular Sturmian theory
JF  - Applied Mathematics in Science and Engineering
VL  - 33
IS  - 1
SP  - 1-39
EP  - 1-39
PB  - Taylor & Francis Ltd
SN  - 27690911
KW  - Symmetric matrix-valued function
KW  - limit theorem
KW  - Moore–Penrose pseudoinverse
KW  - linear hamiltonian system
KW  - Sturmian theory
KW  - Wronskian
KW  - Lidskii angles
KW  - principal solution at infinity
UR  - https://doi.org/10.1080/27690911.2025.2494577
N2  - 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.
ER  -

ŠEPITKA, Peter a Roman ŠIMON HILSCHER. Monotonicity and limit results for certain symmetric matrix-valued functions with applications in singular Sturmian theory. \textit{Applied Mathematics in Science and Engineering}. Taylor \&{} Francis Ltd, 2025, roč.~33, č.~1, s.~1-39. ISSN~2769-0911. Dostupné z: https://dx.doi.org/10.1080/27690911.2025.2494577.

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