The resolvent for Laplace-type operators on asymptotically conic spaces

Hassell, Andrew, and Vasy, András. "The resolvent for Laplace-type operators on asymptotically conic spaces." Annales de l’institut Fourier 51.5 (2001): 1299-1346. <http://eudml.org/doc/115949>.

@article{Hassell2001,
abstract = {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 $H =\Delta + P$, where $\Delta $ is the Laplacian with respect to $g$ and $P$ is a self-adjoint first order scattering differential operator with coefficients vanishing at $\partial X$ 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 $H$, $R(\sigma + i0)$, for $\sigma $ 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.},
affiliation = {Australian National University, Centre for Mathematics and its Applications, Canberra ACT 0200 (Australie); Massachusetts Institute of Technology, Department of Mathematics, Cambridge MA (USA)},
author = {Hassell, Andrew, Vasy, András},
journal = {Annales de l’institut Fourier},
keywords = {Legendre distributions; symbol calculus; scattering metrics; resolvent kernel},
language = {eng},
number = {5},
pages = {1299-1346},
publisher = {Association des Annales de l'Institut Fourier},
title = {The resolvent for Laplace-type operators on asymptotically conic spaces},
url = {http://eudml.org/doc/115949},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Hassell, Andrew
AU - Vasy, András
TI - The resolvent for Laplace-type operators on asymptotically conic spaces
JO - Annales de l’institut Fourier
PY - 2001
PB - Association des Annales de l'Institut Fourier
VL - 51
IS - 5
SP - 1299
EP - 1346
AB - 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 $H =\Delta + P$, where $\Delta $ is the Laplacian with respect to $g$ and $P$ is a self-adjoint first order scattering differential operator with coefficients vanishing at $\partial X$ 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 $H$, $R(\sigma + i0)$, for $\sigma $ 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.
LA - eng
KW - Legendre distributions; symbol calculus; scattering metrics; resolvent kernel
UR - http://eudml.org/doc/115949
ER -