The semiclassical resolvent and the propagator for nontrapping scattering metrics
Analysis of PDEs
2007-05-23 v1 Spectral Theory
Abstract
Consider a compact manifold with boundary with a scattering metric or, equivalently, an asymptotically conic manifold . (Euclidean , with a compactly supported metric perturbation, is an example of such a space.) Let be the positive Laplacian on , and a smooth potential on which decays to second order at infinity. In this paper we construct the kernel of the operator , at a nontrapping energy , uniformly for , small, within a class of Legendre distributions on manifolds with codimension three corners. Using this we construct the kernel of the propagator, , as a quadratic Legendre distribution. We also determine the global semiclassical structure of the spectral projector, Poisson operator and scattering matrix.
Keywords
Cite
@article{arxiv.math/0606606,
title = {The semiclassical resolvent and the propagator for nontrapping scattering metrics},
author = {Andrew Hassell and Jared Wunsch},
journal= {arXiv preprint arXiv:math/0606606},
year = {2007}
}