Transactions of the American Mathematical Society

Author(s): David Borthwick; Peter Perry
Journal: Trans. Amer. Math. Soc. 354 (2002), 1215-1231.
MSC (2000): Primary 58J50, 35P25; Secondary 47A40
Posted: October 26, 2001
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Abstract: For a class of manifolds

that includes quotients of real hyperbolic

-dimensional space by a convex co-compact discrete group, we show that the resonances of the meromorphically continued resolvent kernel for the Laplacian on

coincide, with multiplicities, with the poles of the meromorphically continued scattering operator for

. 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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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 58J50, 35P25, 47A40

David Borthwick
Affiliation: Department of Mathematics and Computer Science, Emory University, Atlanta, Georgia 30322
Email: davidb@mathcs.emory.edu

Peter Perry
Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506--0027
Email: perry@ms.uky.edu

DOI: 10.1090/S0002-9947-01-02906-3
PII: S 0002-9947(01)02906-3
Keywords: Scattering resonances, hyperbolic manifolds
Received by editor(s): March 19, 1999
Received by editor(s) in revised form: June 28, 2001
Posted: 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
Copyright of article: Copyright 2001, American Mathematical Society

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