Qi, Jian Gang, The Symmetry of Singular Hamiltonian Differential Operators and Properties of Deficiency Indices, Acta mathematica Sinica. English series (Print) , 22(1), 2006, pp. 41-50
The symmetry of singular Hamiltonian differential operators is proved under the standard "definiteness condition", which is strictly weaker than the densely definite condition used by A. M. Krall. Meanwhile, some properties of deficiency indices are given.