Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharp resolvent bounds and resonance-free regions   In this note, we consider semiclassical scattering on a manifold which is
Euclidean near infinity or asymptotically hyperbolic. We show that, if the
cut-off resolvent satisfies polynomial estimates in a strip of size $O(h |\log
h|^{-\alpha})$ below the real axis, for some $\alpha\geq 0$, then the cut-off
resolvent is actually bounded by $O(|\log h|^{\alpha+1} h^{-1})$ in this strip.
As an application, we improve slightly the estimates on the real axis given by
Bourgain and Dyatlov in the case of convex co-compact surfaces.

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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: cs
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th