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

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Publikace nespadá pod Filozofickou fakultu, ale pod Přírodovědeckou fakultu. Oficiální stránka publikace je na webu muni.cz.
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ŠEPITKA Peter ŠIMON HILSCHER Roman

Rok publikování 2021
Druh Článek v odborném periodiku
Časopis / Zdroj Journal of Differential Equations
Fakulta / Pracoviště MU

Přírodovědecká fakulta

Citace
www https://doi.org/10.1016/j.jde.2021.06.037
Doi http://dx.doi.org/10.1016/j.jde.2021.06.037
Klíčová slova Linear Hamiltonian system; Lidskii angle; Focal point; Principal solution; Sturmian separation theorem; Limit theorem
Popis 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.
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