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Local smoothing for scattering manifolds with hyperbolic trapped sets. (English) Zbl 1189.58016
For a noncompact complete Riemannian manifold, an effective way to understand its spectrum is to study its resolvent. A particular nice class of manifolds to which the method of microlocal analysis can be applied is the class of scattering manifolds, introduced by Richard Melrose. The author proves an estimate for the resolvent of a scattering manifold with a hyperbolic trapped set and deduces local smoothing for \(L^2\)-functions.

MSC:
58J50 Spectral problems; spectral geometry; scattering theory on manifolds
58J40 Pseudodifferential and Fourier integral operators on manifolds
47G30 Pseudodifferential operators
35P25 Scattering theory for PDEs
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