Completeness of Eigenfunction Systems for Off-Diagonal Infinite-Dimensional Hamiltonian Operators

For the off-diagonal infinite dimensional Hamiltonian operators, which haveat most countable eigenvalues, a necessary and sufficient conditionof the eigenfunction systems to be complete in the sense of Cauchyprincipal value is presented by using the spectral symmetry and neworthogonal relationship of the operators. Moreover, the above resultis extended to a more general case. At last, the completeness of eigenfunction systems for the operators arising from the isotropic plane magnetoelectroelastic solids is described to illustrate the effectiveness of the criterion. The whole results offer theoretical guarantee for separation of variables in Hamiltonian system for some mechanics equations.