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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 ± of a symmetric first-order system Jf ' +Bf=λHf on an interval I, where I= or I= ± . 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.

37J05Relations of dynamical systems with symplectic geometry and topology
34B24Sturm-Liouville theory
47E05Ordinary differential operators