TY - JOUR
T1 - Scattering poles for asymptotically hyperbolic manifolds
AU - Borthwick, David
AU - Perry, Peter
PY - 2002
Y1 - 2002
N2 - 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 the resonances of the meromorphically continued resolvent kernel for the Laplacian on X coincide, with multiplicities, with the poles of the meromorphically 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 resolvent resonances and scattering poles are simple for generic potential perturbations.
AB - 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 the resonances of the meromorphically continued resolvent kernel for the Laplacian on X coincide, with multiplicities, with the poles of the meromorphically 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 resolvent resonances and scattering poles are simple for generic potential perturbations.
KW - Hyperbolic manifolds
KW - Scattering resonances
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U2 - 10.1090/S0002-9947-01-02906-3
DO - 10.1090/S0002-9947-01-02906-3
M3 - Article
AN - SCOPUS:0035993972
SN - 0002-9947
VL - 354
SP - 1215
EP - 1231
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 3
ER -