Scattering Poles for Asymptotically Hyperbolic Manifolds
نویسنده
چکیده
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.
منابع مشابه
Scattering Poles for Asymptotically Hyperbolic Manifolds
Scattering poles for a convex obstacle in the Euclidean space have been extensively studied starting with the work of Watson ’18, with more recent results by Hargé–Lebeau ’94 , Sjöstrand–Zworski ’99 and Jin ’15. In contrast, practically nothing is known for the same problem in hyperbolic space. I will explain the difficulties involved in that and use them as a platform to present a modified ver...
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