  We consider the analytic continuation of the transfer function for a 2x2
matrix Hamiltonian into the unphysical sheets of the energy Riemann surface. We
construct non-selfadjoint operators representing operator roots of the transfer
function which reproduce certain parts of its spectrum including resonances
situated in the unphysical sheets neighboring the physical sheet. On this
basis, completeness and basis properties for the root vectors of the transfer
function (including those for the resonances) are proved.
