Friedrichs extensions for singular Hamiltonian operators with intermediate deficiency indices

For singular Hamiltonian operators in the intermediate deficiency indices case, we give a complete characterization of Friedrichs extensions of minimal Hamiltonian operators, which unifies and generalizes some known results in the literature. The exact boundary conditions for the Friedrichs extensions are constructed via the principal solutions. The main approach in this paper is the Friedrichs construction by way of the refined LC-type solutions at singular endpoints.