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Microlocal analysis of asymptotically hyperbolic and Kerr-de Sitter spaces (with an appendix by Semyon Dyatlov)
In this paper we develop a general, systematic, microlocal framework for the Fredholm analysis of non-elliptic problems, including high energy (or semiclassical) estimates, which is stable underExpand
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Microlocal analysis of asymptotically hyperbolic spaces and high energy resolvent estimates
In this paper we describe a new method for analyzing the Laplacian on asymptotically hyperbolic spaces, which was introduced recently by the author. This new method in particular constructs theExpand
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The spectral projections and the resolvent for scattering metrics
In this paper, we consider a compact manifold with boundaryX equipped with a scattering metricg as defined by Melrose [9]. That is,g is a Riemannian metric in the interior ofX that can be brought toExpand
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The wave equation on asymptotically anti de Sitter spaces
In this paper we describe the behavior of solutions of the KleinGordon equation, ( g + λ)u = f , on Lorentzian manifolds (X, g) which are anti-de Sitter-like (AdS-like) at infinity. Such manifoldsExpand
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Semiclassical Estimates¶in Asymptotically Euclidean Scattering
Abstract: We consider long range semiclassical perturbations of the Laplacian on asymptotically Euclidean manifolds. We obtain precise resolvent estimates under non-trapping assumptions. The noveltyExpand
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Semilinear wave equations on asymptotically de Sitter, Kerr–de Sitter and Minkowski spacetimes
In this paper we show the small data solvability of suitable semilinear wave and Klein-Gordon equations on geometric classes of spaces, which include so-called asymptotically de Sitter and Kerr-deExpand
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Propagation of singularities in many-body scattering
Abstract In this paper we describe the propagation of singularities of tempered distributional solutions u∈ S ′ of (H−λ)u=0, λ>0, where H is a many-body Hamiltonian H=Δ+V, Δ⩾0, V=∑aVa, under theExpand
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Analytic continuation of the resolvent of the Laplacian on symmetric spaces of noncompact type
Let (M,g) be a globally symmetric space of noncompact type, of arbitrary rank, and Δ its Laplacian. We introduce a new method to analyze Δ and the resolvent (Δ-σ)-1; this has origins in quantumExpand
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Boundary rigidity with partial data
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 ofExpand
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The wave equation on asymptotically de Sitter-like spaces
In this paper we obtain the asymptotic behavior of solutions of the Klein–Gordon equation on Lorentzian manifolds (X○,g) which are de Sitter-like at infinity. Such manifolds are Lorentzian analoguesExpand
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