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 of the Eigenfunctions of the Absolutely Continuous Spectrum

In the present work, we consider the scattering problem of three one-dimensional quantum particles of equal mass interacting by pair finite potentials such that each pair subsystem permits a bound state. We study the limit values of the Schrödinger operator resolvent integral kernel as the spectral parameter approaches the positive semiaxis, which allows us to construct the asymptotics of eigenfunctions of the absolutely continuous spectrum.