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

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

2005-02-18

arxiv.org/abs/math/0502398v3

Mathematics

Analysis of PDEs

Revised based on referee comments. While there are no substantial changes, the readability has been improved, a number of typo

Scientific paper

In this paper, the scattering and spectral theory of $H=\Delta_g+V$ is developed, where $\Delta_g$ 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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