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

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Monotonicity and limit results for certain symmetric matrix-valued functions with applications in singular Sturmian theory
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA23-05242S" target="_blank" >GA23-05242S: Oscillation theory on hybrid time domains with applications in spectral theory and matrix analysis</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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