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Microlocal propagation near radial points and scattering for symbolic potentials of order zero

Andrew Hassell·Richard Melrose·Andras Vasy
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Abstract

In this paper, the scattering and spectral theory of $H=Δ_g+V$ is developed, where $Δ_g$ is the Laplacian with respect to a scattering metric $g$ on a compact manifold $X$ with boundary and $V\in C^\infty(X)$ is real; this extends our earlier results in the two-dimensional case. Included in this class of operators are perturbations of the Laplacian on Euclidean space by potentials homogeneous of degree zero near infinity. Much of the particular structure of geometric scattering theory can be traced to the occurrence of radial points for the underlying classical system; a general framework for microlocal analysis at these points forms the main part of the paper.

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Andrew Hassell, Richard Melrose, Andras Vasy. 2008-09-12. Microlocal propagation near radial points and scattering for symbolic potentials of order zero. https://arxiv.org/abs/math/0502398

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