The resolvent for Laplace-type operators on asymptotically conic spaces

Andrew Hassell; András Vasy

Displaying similar documents to “The resolvent for Laplace-type operators on asymptotically conic spaces”

Estimates on the number of scattering poles near the real axis for strictly convex obstacles

Johannes Sjöstrand, Maciej Zworski (1993)

Annales de l'institut Fourier

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For the Dirichlet Laplacian in the exterior of a strictly convex obstacle, we show that the number of scattering poles of modulus $\leq r$ in a small angle $θ$ near the real axis, can be estimated by Const $θ^{3 / 2} r^{n}$ for $r$ sufficiently large depending on $θ$ . Here $n$ is the dimension.

Scattering matrix for asymptotically euclidean manifolds

Richard Melrose, Maciej Zworski (1994)

Journées équations aux dérivées partielles

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Propagation of singularities in many-body scattering

András Vasy (2001)

Annales scientifiques de l'École Normale Supérieure

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Resonances for strictly convex obstacles

Johannes Sjöstrand (1997-1998)

Séminaire Équations aux dérivées partielles

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On considère le problème de Dirichlet à l’éxtérieur d’un obstacle strictement convexe borné à bord $C^{\infty}$ . Sous une hypothèse sur la variation de la courbure, on obtient à un facteur $1 + o (1)$ près, le nombre de résonances de module $\leq r$ , associées à la première racine de la fonction d’Airy.

Propagation of singularities in many-body scattering in the presence of bound states

András Vasy (1999)

Journées équations aux dérivées partielles

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In these lecture notes we describe the propagation of singularities of tempered distributional solutions $u \in 𝒮^{'}$ of $(H - λ) u = 0$ , where $H$ is a many-body hamiltonian $H = Δ + V$ , $Δ \geq 0$ , $V = \sum_{a} V_{a}$ , and $λ$ is not a threshold of $H$ , under the assumption that the inter-particle (e.g. two-body) interactions $V_{a}$ are real-valued polyhomogeneous symbols of order $- 1$ (e.g. Coulomb-type with the singularity at the origin removed). Here the term “singularity” provides a microlocal description of the lack of decay at infinity. Our result is...