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On the deficiency indices and self-adjointness of symmetric Hamiltonian systems. (English) Zbl 1016.37026

From the authors’ abstract: The main purpose of this paper is to investigate the formal deficiency indices \(N_\pm\) of a symmetric first-order system \(Jf'+Bf =\lambda Hf\) on an interval \(I\), where \(I=\mathbb{R}\) or \(I= \mathbb{R}_\pm\). We obtain two results for such a system to have minimal numbers and a criterion for their maximality. We also obtain a generalization of the well-known Titchmarsh-Sears theorem for second-order Sturm-Liouville-type equations. This contains results due to Lidskij and Krein as special cases.

MSC:

37J05 Relations of dynamical systems with symplectic geometry and topology (MSC2010)
34B24 Sturm-Liouville theory
47E05 General theory of ordinary differential operators
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