Spectral Properties at a Threshold for Two-Channel Hamiltonians

Spectral properties and scattering theory in the low-energy limit are investigated for two-channel Hamiltonians with Schr¨odinger operators as component Hamiltonians. In various, mostly fairly ‘‘singular’’ settings asymptotic expansions of the resolvent are deduced as the spectral parameter tends to the threshold zero. Furthermore scattering theory for pairs of two-channel Hamiltonians is established. As an application of the expansions of the resolvent, asymptotic expansions of the scattering matrix are derived as the energy parameter tends to the threshold zero.