Banded matrices and discrete Sturm-Liouville eigenvalue problems.
Zur Unlösbarkeit linearer partieller Differentialgleichungen.
Quadratic functionals: positivity, oscillation, Rayleigh's principle
In this paper we give a survey on the theory of quadratic functionals. Particularly the relationships between positive definiteness and the asymptotic behaviour of Riccati matrix differential equations, and between the oscillation properties of linear Hamiltonian systems and Rayleigh’s principle are demonstrated. Moreover, the main tools form control theory (as e.g. characterization of strong observability), from the calculus of variations (as e.g. field theory and Picone’s identity), and from matrix...
Sturm-Liouville difference equations and banded matrices
Asymptotic behaviour of Riccati's differential equation associated with self-adjoint scalar equations of even order
Rayleigh principle for linear Hamiltonian systems without controllability
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. The main tools...
Rayleigh principle for linear Hamiltonian systems without controllability
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. The main tools...
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