Displaying similar documents to “Quadratic functionals: positivity, oscillation, Rayleigh's principle”

Rayleigh principle for linear Hamiltonian systems without controllability

Werner Kratz, Roman Šimon Hilscher (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we consider linear Hamiltonian differential systems without the controllability (or normality) assumption. We prove the Rayleigh principle for these systems with Dirichlet boundary conditions, which provides a variational characterization of the finite eigenvalues of the associated self-adjoint eigenvalue problem. This result generalizes the traditional Rayleigh principle to possibly abnormal linear Hamiltonian systems....

Rayleigh principle for linear Hamiltonian systems without controllability

Werner Kratz, Roman Šimon Hilscher (2012)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

In this paper we consider linear Hamiltonian differential systems without the controllability (or normality) assumption. We prove the Rayleigh principle for these systems with Dirichlet boundary conditions, which provides a variational characterization of the finite eigenvalues of the associated self-adjoint eigenvalue problem. This result generalizes the traditional Rayleigh principle to possibly abnormal linear Hamiltonian systems....