Mathematical Research Letters

Volume 21 (2014)

Number 6

Non-trapping estimates near normally hyperbolic trapping

Pages: 1277 – 1304

DOI: https://dx.doi.org/10.4310/MRL.2014.v21.n6.a5

Authors

Peter Hintz (Department of Mathematics, Stanford University, Stanford, California, U.S.A.)

Andras Vasy (Department of Mathematics, Stanford University, Stanford, California, U.S.A.)

Abstract

In this paper, we prove semiclassical resolvent estimates for operators with normally hyperbolic trapping which are lossless relative to non-trapping estimates but take place in weaker function spaces. In particular, we obtain non-trapping estimates in standard $L^2$ spaces for the resolvent sandwiched between operators which localize away from the trapped set $\Gamma$ in a rather weak sense, namely whose principal symbols vanish on $\Gamma$.

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Accepted 18 July 2014

Published 2 April 2015