The resolvent for Laplace-type operators on asymptotically conic spaces
| dc.creator | Hassell, Andrew | |
| dc.creator | Vasy, Andras | |
| dc.date | 2000-02-15 | |
| dc.date.accessioned | 2026-07-07T04:33:52Z | |
| dc.date.available | 2026-07-07T04:33:52Z | |
| dc.description | Let X be a compact manifold with boundary, and g a scattering metric on X, which may be either of short range or `gravitational' long range type. Thus, g gives X the geometric structure of a complete manifold with an asymptotically conic end. Let H be an operator of the form $H = Δ+ P$, where $Δ$ is the Laplacian with respect to g and P is a self-adjoint first order scattering differential operator with coefficients vanishing at the boundary of X and satisfying a `gravitational' condition. We define a symbol calculus for Legendre distributions on manifolds with codimension two corners and use it to give a direct construction of the resolvent kernel of H, $R(σ+ i0)$, for $σ$ on the positive real axis. In this approach, we do not use the limiting absorption principle at any stage; instead we construct a parametrix which solves the resolvent equation up to a compact error term and then use Fredholm theory to remove the error term. | |
| dc.description | 34 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0002114 | |
| dc.identifier | http://arxiv.org/abs/math/0002114 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/58688 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35P20, 58J40 | |
| dc.title | The resolvent for Laplace-type operators on asymptotically conic spaces | |
| dc.type | text |