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From resolvent estimates to damped waves
resolvent estimates damped waves Analysis of PDEs
2012/6/29
In this paper we show how to obtain decay estimates for the damped wave equation on a compact manifold without geometric control via knowledge of the dynamics near the un-damped set. We show that if r...
Semiclassical resolvent estimates at trapped sets
Resolvent estimates trapping propagation of singularities
2012/6/21
We extend our recent results on propagation of semiclassical resolvent estimates through trapped sets when a priori polynomial resolvent bounds hold. Previously we obtained non-trapping estimates in t...
Extending cutoff resolvent estimates via propagation of singularities
cutoff resolvent estimates propagation of singularities Analysis of PDEs
2011/9/9
Abstract: We use a gluing method developed in joint work with Andr\'as Vasy to show that polynomially bounded cutoff resolvent estimates at the real axis imply, up to a constant factor, the same estim...