The scattering problem of three one-dimensional short-range quantum particles involving bound states in pair subsystems. The coordinate asymptotics of the resolvent kernel and absolutely continuous spectrum eigenfunctions

In the work the scattering problem of three one-dimensional quantum particles of equal masses interacting by pair finite potentials is considered. The potentials structure allows bound states in the corresponding pair subsystems. The limit values of the Schroedinger operator resolvent kernel are studied, when the spectral parameter sits onto the absolutely continuous spectrum – the positive semi-axis. As a result, the coordinate asymptotics of the absolutely continuous spectrum eigenfunctions are constructed.