A Mourre estimate and related bounds for hyperbolic manifolds with cusps of non-maximal rank

R. Froese; P. Hislop; P. Perry

doi:10.1016/0022-1236(91)90080-O

A Mourre estimate and related bounds for hyperbolic manifolds with cusps of non-maximal rank

R. Froese, P. Hislop, P. Perry

Mathematics

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15 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	292-310
Number of pages	19
Journal	Journal of Functional Analysis
Volume	98
Issue number	2
DOIs	https://doi.org/10.1016/0022-1236(91)90080-O
State	Published - Jun 1991

Bibliographical note

Funding 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.

ASJC Scopus subject areas

Analysis

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10.1016/0022-1236(91)90080-O

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title = "A Mourre estimate and related bounds for hyperbolic manifolds with cusps of non-maximal rank",

abstract = "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.",

author = "R. Froese and P. Hislop and P. Perry",

note = "Funding 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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AU - Froese, R.

AU - Hislop, P.

AU - Perry, P.

N1 - Funding 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.

PY - 1991/6

Y1 - 1991/6

N2 - 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.

AB - 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.

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JF - Journal of Functional Analysis

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A Mourre estimate and related bounds for hyperbolic manifolds with cusps of non-maximal rank

Abstract

Bibliographical note

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