  We show the analytic continuation of the resolvent of the Laplacian on
asymptotically hyperbolic spaces on differential forms, including high energy
estimates in strips. This is achieved by placing the spectral family of the
Laplacian within the framework developed, and applied to scalar problems, by
the author recently, roughly by extending the problem across the boundary of
the compactification of the asymptotically hyperbolic space in a suitable
manner. The main novelty is that the non-scalar nature of the operator is dealt
with by relating it to a problem on an asymptotically Minkowski space to
motivate the choice of the extension across the conformal boundary.
