Limiting absorption principle and equivalence of Feynman propagators on asymptotically Minkowski spacetimes

In this paper, we shall show that the limiting absorption principle for the wave operator on the asymptotically Minkowski spacetime. This problem was previously considered by [A. Vasy, J. Spect. Theory, 10,439-461 , (2020)]. Here, we employ a more transparent tool, the Mourre theory and removes an additional condition which is imposed in his paper. Moreover, we also prove that the anti-Feynman propagator defined by G'erard and Wrochna coincides with the outgoing resolvent.