2005/02/18 by Andrew Hassell, Richard Melrose, Hassell, Andrew +3
Mathematics · #35P25 (Primary) 81UXX (Secondary) #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35P25 #msc:81UXX
paper · pdf · doi:10.48550/arxiv.math/0502398
Revised based on referee comments. While there are no substantial changes, the readability has been improved, a number of typos have been fixed and even some incorrect statements have been corrected. The order of the two phrases in the title has been reversed to indicate their relative importance
In this paper, the scattering and spectral theory of H=Δg+V is developed, where Δg is the Laplacian with respect to a scattering metric g on a compact manifold X with boundary and V∈ C^∞(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.