Local Smoothing for Scattering Manifolds with Hyperbolic Trapped Sets

We prove a resolvent estimate for the Laplace-Beltrami operator on a scattering manifold with a hyperbolic trapped set, and as a corollary deduce local smoothing. We use a result of Nonnenmacher-Zworski to provide an estimate near the trapped region, a result of Burq and Cardoso-Vodev to provide an...

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Vydáno v:Communications in mathematical physics Ročník 286; číslo 3; s. 837 - 850
Hlavní autor: Datchev, Kiril
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer-Verlag 01.03.2009
Springer
Témata:
Classical and Quantum Gravitation
Complex Systems
Exact sciences and technology
Mathematical analysis
Mathematical and Computational Physics
Mathematical methods in physics
Mathematical Physics
Mathematics
Operator theory
Other topics in mathematical methods in physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Sciences and techniques of general use
Several complex variables and analytic spaces
Theoretical
Pseudodifferential Operator
Principal Symbol
Manifold
Local Smoothing
Resolvent Estimate
Laplace operator
Mathematical manifolds
Smoothing methods
Resolvent
Smoothing
Mathematical physics
ISSN:0010-3616, 1432-0916
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Popis
Shrnutí:We prove a resolvent estimate for the Laplace-Beltrami operator on a scattering manifold with a hyperbolic trapped set, and as a corollary deduce local smoothing. We use a result of Nonnenmacher-Zworski to provide an estimate near the trapped region, a result of Burq and Cardoso-Vodev to provide an estimate near infinity, and the microlocal calculus on scattering manifolds to combine the two.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-008-0684-1