Limiting absorption principle on Riemannian scattering (asymptotically conic) spaces, a Lagrangian approach
Analysis of PDEs
2019-07-16 v2 Differential Geometry
Abstract
We use a Lagrangian perspective to show the limiting absorption principle on Riemannian scattering, i.e. asymptotically conic, spaces, and their generalizations. More precisely we show that, for non-zero spectral parameter, the `on spectrum', as well as the `off-spectrum', spectral family is Fredholm in function spaces which encode the Lagrangian regularity of generalizations of `outgoing spherical waves' of scattering theory, and indeed this persists in the `physical half plane'.
Keywords
Cite
@article{arxiv.1905.12587,
title = {Limiting absorption principle on Riemannian scattering (asymptotically conic) spaces, a Lagrangian approach},
author = {Andras Vasy},
journal= {arXiv preprint arXiv:1905.12587},
year = {2019}
}
Comments
42 pages, 4 figures. This version mostly adds some explanations to the first version, but there are some other minor changes as well scattered throughout the text