Scattering poles for asymptotically hyperbolic manifolds

Citation
D. Borthwick et P. Perry, Scattering poles for asymptotically hyperbolic manifolds, T AM MATH S, 354(3), 2002, pp. 1215-1231
Citations number
33
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Mathematics
Journal title
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN journal
0002-9947 → ACNP
Volume
354
Issue
3
Year of publication
2002
Pages
1215 - 1231
Database
ISI
SICI code
0002-9947(2002)354:3<1215:SPFAHM>2.0.ZU;2-9
Abstract
For a class of manifolds X that includes quotients of real hyperbolic (n 1)-dimensional space by a convex co-compact discrete group, we show that th e resonances of the meromorphically continued resolvent kernel for the Lapl acian on X coincide, with multiplicities, with the poles of the meromorphic ally continued scattering operator for X. In order to carry out the proof, we use Shmuel Agmon's perturbation theory of resonances to show that both r esolvent resonances and scattering poles are simple for generic potential p erturbations.