We consider the Laplace operator on quotients of hyperbolic n-dimensional space by a geometrically finite discrete group of hyperbolic isometries with parabolic subgroups of non-maximal rank. Using methods developed by the first two authors, we prove a "Mourre estimate" and commutator estimates on the Laplacian which imply absolute continuity of the spectrum and quantitative resolvent estimates. These estimates will be used elsewhere to study the scattering matrix and Eisenstein series and their meromorphic continuations, and should be useful in studying trace formulas for these discrete groups.
|Number of pages||19|
|Journal||Journal of Functional Analysis|
|State||Published - Jun 1991|
Bibliographical noteFunding Information:
We thank Peter Sarnak and Richard Schoen for thier hospitality at Stanford University, and Rafe Mazzeo and Ralph Phillips for useful conversations. R. F. would like to thank Werner Kirsch for his hospitality at the Ruhruniversitat Bochum during the time this paper was being written. This project was partially supported by NSF Grant R II-8610671 and the Commonwealth of Kentucky through the Kentucky EPSCoR Program.
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