We consider a non-trapping n-dimensional Lorentzian manifold endowed with an end structure modeled on the radial compactification of Minkowski space. We find a full asymptotic expansion for tempered… (More)

In this paper we describe a new method for analyzing the Laplacian on asymptotically hyperbolic spaces, which was introduced in [18]. This new method in particular constructs the analytic… (More)

In this paper we obtain the asymptotic behavior of solutions of the Klein-Gordon equation on Lorentzian manifolds (X, g) which are de Sitterlike at infinity. Such manifolds are Lorentzian analogues… (More)

We use semiclassical propagation of singularities to give a general method for gluing together resolvent estimates. As an application we prove estimates for the analytic continuation of the resolvent… (More)

We study the boundary rigidity problem with partial data consisting of determining locally the Riemannian metric of a Riemannian manifold with boundary from the distance function measured at pairs of… (More)

In this paper we construct a parametrix for the high-energy asymptotics of the analytic continuation of the resolvent on a Riemannian manifold which is a small perturbation of the Poincaré metric on… (More)

In this paper, the scattering and spectral theory of H = ∆g + V is developed, where ∆g is the Laplacian with respect to a scattering metric g on a compact manifold X with boundary and V ∈ C(X) is… (More)

In this paper we consider a compact manifold with boundary X equipped with a scattering metric g as defined by Melrose [9]. That is, g is a Riemannian metric in the interior of X that can be brought… (More)

We investigate the geometric propagation and diffraction of singularities of solutions to the wave equation on manifolds with edge singularities. This class of manifolds includes, and is modelled on,… (More)

In this paper an asymptotic expansion is proved for locally (at infinity) outgoing functions on asymptotically Euclidian spaces. This is applied to N-body scattering where the two-body interactions… (More)