Monotonicity and limit results for certain symmetric matrix-valued functions with applications in singular Sturmian theory
| Authors | |
|---|---|
| Year of publication | 2025 |
| Type | Article in Periodical |
| Magazine / Source | Applied Mathematics in Science and Engineering |
| MU Faculty or unit | |
| Citation | |
| web | https://doi.org/10.1080/27690911.2025.2494577 |
| 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 |
| 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. |
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