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NON-TRAPPING ESTIMATES NEAR NORMALLY HYPERBOLIC TRAPPING

Peter Hintz, András Vasy

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Abstract

Abstract. In this paper we prove semiclassical resolvent estimates for op-erators 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 L2 spaces for the resolvent sand-wiched between operators which localize away from the trapped set Γ in a rather weak sense, namely whose principal symbols vanish on Γ. 1.

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What this paper is about

Abstract. In this paper we prove semiclassical resolvent estimates for op-erators 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 L2 spaces for the resolvent sand-wiched between operators which localize away from the trapped set Γ in a rather weak sense, namely whose principal symbols vanish on Γ. 1.

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Available abstract

Abstract. In this paper we prove semiclassical resolvent estimates for op-erators 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 L2 spaces for the resolvent sand-wiched between operators which localize away from the trapped set Γ in a rather weak sense, namely whose principal symbols vanish on Γ. 1.

Key concepts: Trapping, Resolvent, Mathematics, Semiclassical physics, Set (abstract data type), Function (biology), Extension (predicate logic), Mathematical analysis

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