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Lidskii angles and Sturmian theory for linear Hamiltonian systems on compact interval
- Source :
- Journal of Differential Equations. 298:1-29
- Publication Year :
- 2021
- Publisher :
- Elsevier BV, 2021.
-
Abstract
- 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.
- Subjects :
- Pure mathematics
Basis (linear algebra)
Applied Mathematics
010102 general mathematics
Monotonic function
06 humanities and the arts
0603 philosophy, ethics and religion
01 natural sciences
Hamiltonian system
Monotone polygon
Fundamental matrix (linear differential equation)
060302 philosophy
Linear algebra
0101 mathematics
Legendre polynomials
Analysis
Mathematics
Symplectic geometry
Subjects
Details
- ISSN :
- 00220396
- Volume :
- 298
- Database :
- OpenAIRE
- Journal :
- Journal of Differential Equations
- Accession number :
- edsair.doi...........f430540488f529e0d103fb0081729802