Resolvent and Spectral Measure on Non-Trapping Asymptotically Hyperbolic Manifolds II: Spectral Measure, Restriction Theorem, Spectral Multipliers

Xi Chen, Andrew Hassell

Type: Article

Publication Date: 2018-01-01

Citations: 22

DOI: https://doi.org/10.5802/aif.3183

Abstract

We consider the Laplacian Δ on an asymptotically hyperbolic manifold X, as defined by Mazzeo and Melrose. We give pointwise bounds on the Schwartz kernel of the spectral measure for the operator (Δ-n 2 /4) + 1/2 on such manifolds, under the assumptions that X is nontrapping and there is no resonance at the bottom of the spectrum. This uses the construction of the resolvent given by Mazzeo and Melrose, Melrose, Sá Barreto and Vasy, the present authors, and Wang.

Locations

French digital mathematics library (Numdam) - View - PDF
ANU Open Research (Australian National University) - View - PDF
Annals of the Fourier Institute (Institut Fourier) - View - PDF
Annales de l’institut Fourier - View - PDF

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+ PDF Chat	The Hodge cohomology of a conformally compact metric	1988	Rafe Mazzeo
+	Classical and modern Fourier analysis	2003	Loukas Grafakos
+	Spectral properties of Schrödinger operators and time-decay of the wave functions	1979	Arne Jensen Tosio Kato
+ PDF Chat	Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds	1982	Jeff Cheeger M. Gromov Michael E. Taylor
+ PDF Chat	Resolvent and spectral measure on non-trapping asymptotically hyperbolic manifolds I: Resolvent construction at high energy	2015	Xi Chen Andrew Hassell
+	Partial Differential Equations II: Qualitative Studies of Linear Equations	1996	Michael E. Taylor
+	Unique Continuation at Infinity and Embedded Eigenvalues for Asymptotically Hyperbolic Manifolds	1991	Rafe Mazzeo
+ PDF Chat	The spectral projections and the resolvent for scattering metrics	1999	Andrew Hassell András Vasy
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