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Scattering poles for asymptotically hyperbolic manifolds

Authors: David Borthwick and Peter Perry
Journal: Trans. Amer. Math. Soc. 354 (2002), 1215-1231
MSC (2000): Primary 58J50, 35P25; Secondary 47A40
Published electronically: October 26, 2001
MathSciNet review: 1867379
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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 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.

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Additional Information

David Borthwick
Affiliation: Department of Mathematics and Computer Science, Emory University, Atlanta, Georgia 30322

Peter Perry
Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506–0027

Keywords: Scattering resonances, hyperbolic manifolds
Received by editor(s): March 19, 1999
Received by editor(s) in revised form: June 28, 2001
Published electronically: October 26, 2001
Additional Notes: Supported in part by NSF grant DMS-9796195 and by an NSF Postdoctoral Fellowship.
Supported in part by NSF grant DMS-9707051
Article copyright: © Copyright 2001 American Mathematical Society

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