To the question of Schröedinger operator kernel resolvent asymptotics construction in the three one-dimensional quantum particles scattering problem interacting by finite repulsive pair potentials

The present work aims at announcing a new approach to a construction of the asymptotics (at infinity in configuration space) of the Schrödinger operator resolvent kernel asymptotics in the scattering problem of three one-dimensional quantum particles interacting by the finite pair repulsive potentials. Within the framework of this approach the asymptotics of Schrödinger operator absolutely continuum spectrum eigenfunctions can be constructed explicitly. We should emphasize that the restriction of the consideration for the case of finite pair potentials does not lead to a simplification of the problem in its essence as the potential of the interaction of all three particles remains non-decreasing at infinity but allows to put aside a certain number of technical details.