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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. The main tools...
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...
In this paper, we present a new point of view on the renormalization of some exponential sums stemming from number theory. We generalize this renormalization procedure to study some matrix cocycles arising in spectral problems of quantum mechanics
We consider a second order regular differential operator whose coefficients are nonselfadjoint bounded operators acting in a Hilbert space. An estimate for the resolvent and a bound for the spectrum are established. An operator is said to be stable if its spectrum lies in the right half-plane. By the obtained bounds, stability and instability conditions are established.
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