English

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