Resonance free regions for nontrapping manifolds with cusps

Abstract

We prove resolvent estimates for nontrapping manifolds with cusps which imply the existence of arbitrarily wide resonance free strips, local smoothing for the Schrodinger equation, and resonant wave expansions. We obtain lossless limiting absorption and local smoothing estimates, but the estimates on the holomorphically continued resolvent exhibit losses. We prove that these estimates are optimal in certain respects.

45 pages, 6 figures

References in corpus (4)

• Asymptotics of linear waves and resonances with applications to black holes
• Resonance projectors and asymptotics for r-normally hyperbolic trapped sets
• Restriction Bounds for the Free Resolvent and Resonances in Lossy Scattering
• Wave decay on convex co-compact hyperbolic manifolds

Cited by in corpus (1)

• Spectral gaps, additive energy, and a fractal uncertainty principle