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Sturmian theory for linear Hamiltonian systems without controllability

✍ Scribed by Roman Šimon Hilscher

Publisher: John Wiley and Sons
Year: 2011
Tongue: English
Weight: 148 KB
Volume: 284
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.201000071

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✦ Synopsis

In this paper we present Sturmian separation and comparison theorems for linear Hamiltonian systems when no controllability assumption is imposed. This generalizes the traditional results of W. T. Reid for controllable (or normal) linear Hamiltonian systems to the possibly abnormal case. Our new theory is based on several recent results on linear Hamiltonian systems without controllability by W. Kratz, M. Wahrheit, V. Zeidan, and the author regarding the piecewise constant kernel for conjoined bases, the oscillation and eigenvalue theorems, and the Rayleigh principle.

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