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Geometric characterization of singular self-adjoint boundary conditions for Hamiltonian systems. (English) Zbl 0872.34010

The selfadjoint realizations with separated boundary conditions of rather general differential expressions on an interval \([a,b)\) with \(a\) regular and \(b\) singular are investigated. The permissible boundary conditions at the singular endpoint are first described in terms of the square integrable solutions of the associated differential equation. Then, for arbitrary (equal) deficiency indices, they are characterized using the \(M\)-functions lying on the boundary of the limiting object of the Weyl circles, thus generalizing a well-known result for Sturm-Liouville operators.

MSC:

34B20 Weyl theory and its generalizations for ordinary differential equations
47E05 General theory of ordinary differential operators
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References:

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