The Laplace operator on a hyperbolic manifold I. Spectral and scattering theory

Peter Perry

Type: Article

Publication Date: 1987-11-01

Citations: 46

DOI: https://doi.org/10.1016/0022-1236(87)90110-8

View Publication

Locations

Journal of Functional Analysis - View

Similar Works

Action	Title	Year	Authors
+	A Mourre estimate and related bounds for hyperbolic manifolds with cusps of non-maximal rank	1991	Richard Froese Peter D. Hislop Peter Perry
+	Hyperbolic Eisenstein series on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e20" altimg="si1.svg"><mml:mi>n</mml:mi></mml:math>-dimensional hyperbolic spaces	2019	Yosuke Irie
+	<i>L</i> <sup> <i>p</i> </sup> Spectral Theory for Manifolds of Hyperbolic Type	1996	N. Mandouvalos Michel Marias
+	The Laplace operator on a hyperbolic manifold. II. Eisenstein series and the scattering matrix.	1989	Peter Perry
+	Hyperbolic Dirac and Laplace operators on examples of hyperbolic spin manifolds	2012	Denis Constales Rolf Sören Kraußhar John Ryan
+	Spectral theory of the Laplace operator on manifolds with generalized cusps	2010	Nikolaos Roidos
+	Lp spectral theory of Kleinian groups	1988	E. B. Davies Barry Simon Michael E. Taylor
+	Relationship between the Discrete and Resonance Spectrum for the Laplace Operator on a Noncompact Hyperbolic Riemann Surface	2019	Дмитрий Александрович Попов
+	Eigenspaces of the Laplacian on hyperbolic spaces: Composition series and integral transforms	1987	Henrik Schlichtkrull
+	The spectral characteristics of Laplace-Beltrami operators in hyperbolic spaces	1991	Leonid Parnovski
+ PDF Chat	On the spectral theory and dynamics of asymptotically hyperbolic manifolds	2010	Julie Rowlett
+	Resolvent of the Laplacian on geometrically finite hyperbolic manifolds	2011	Colin Guillarmou Rafe Mazzeo
+	The spectral asymptotics of elliptic operators of Schr�dinger type on a hyperbolic space	1992	D. V. Efremov Mikhail Shubin
+ PDF Chat	Hyperbolic Eisenstein Series for Geometrically Finite Hyperbolic Surfaces of Infinite Volume	2022	Thérèse Falliero
+	Hyperbolic Eisenstein series for geometrically finite hyperbolic surfaces of infinite volume	2012	Thérèse Falliero
+ PDF Chat	Scattering and inverse scattering on ACH manifolds	2008	Colin Guillarmou Antônio Sá Barreto
+	Eigenfunctions of the Laplacian on a hermitian hyperbolic space	1974	Katsuhiro Minemura
+	On the spectrum of the Laplace-Beltrami operator for p-forms on asymptotically hyperbolic manifolds	2003	Francesca Antoci
+ PDF Chat	The spectrum of the Laplace operator on conformally flat manifolds	1985	Grigorios Tsagas
+	Resonances and residue operators for pseudo-Riemannian hyperbolic spaces	2023	Jan Frahm Polyxeni Spilioti

Works That Cite This (45)

Action	Title	Year	Authors
+ PDF Chat	Introduction to Spectral Theory and Inverse Problem on Asymptotically Hyperbolic Manifolds	2014	Hiroshi Isozaki Yaroslav Kurylev
+	Spectral analysis of second-order elliptic operators on noncompact manifolds	1989	Richard Froese Peter D. Hislop
+	Zeta Functions and Periodic Orbit Theory: A Review	1993	Norman E. Hurt
+	Scattering operator and Eisenstein integral for Kleinian groups	1990	N. Mandouvalos
+ PDF Chat	Conic singularities, generalized scattering matrix, and inverse scattering on asymptotically hyperbolic surfaces	2014	Hiroshi Isozaki Yaroslav Kurylev Matti Lassas
+	The Spectrum of Kleinian Manifolds	2000	Ulrich Bunke Martin Olbrich
+	A Mourre estimate and related bounds for hyperbolic manifolds with cusps of non-maximal rank	1991	Richard Froese Peter D. Hislop Peter Perry
+	Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature	1987	Rafe Mazzeo Richard Melrose
+	Scattering theory for the wave equation on a hyperbolic manifold	1987	Ralph S. Phillips Bettina Wiskott Alex Woo
+ PDF Chat	Inverse spectral problems on hyperbolic manifolds and their applications to inverse boundary value problems in Euclidean space	2004	Hiroshi Isozaki

Works Cited by This (33)

Action	Title	Year	Authors
+	Nonlinear Analysis on Manifolds. Monge-Ampère Equations	1982	Thierry Aubin
+	Scattering theory on real hyperbolic spaces and their compact perturbations	1980	Alex Woo
+	The geometry and topology of three-manifolds	1979	William P. Thurston
+	The Selberg Trace Formula and Related Topics	1986	Dennis A. Hejhal Peter Sarnak Audrey Terras
+	Methods of Modern Mathematical Physics	1972	Michael C. Reed Barry Simon
+	Scattering theory and automorphic functions	2008	Gilles Lachaud
+	Fourier coefficients of the resolvent for a Fuchsian group.	1977	John D. Fay
+	On cusp forms for co-finite subgroups ofPSL(2,?)	1985	Ralph S. Phillips Peter Sarnak
+	Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature	1987	Rafe Mazzeo Richard Melrose
+	Scattering theory and automorphic functions	1975	B. S. Pavlov L. D. Faddeev