Resolvent and Radiation Fields on Non-trapping Asymptotically Hyperbolic Manifolds

Abstract

We construct a semi-classical parametrix for the Laplacian on non-trapping asymptotically hyperbolic manifolds, which generalizes the construction of Melrose, Sa Barreto and Vasy. As applications, we obtain high energy resolvent estimates and resonance free strips. Also, we prove that the Friedlander radiation field decays exponentially for initial data in proper spaces.

26 pages

References in corpus (1)

• The Scattering Relation on Asymptotically Hyperbolic Manifolds

Cited by in corpus (3)

• Resolvent and spectral measure on non-trapping asymptotically hyperbolic manifolds II: spectral measure, restriction theorem, spectral multiplier
• Resolvent and spectral measure on non-trapping asymptotically hyperbolic manifolds I: Resolvent construction at high energy
• The scattering operator on asymptotically hyperbolic manifolds