Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rough Potential Recovery in the Plane   We reconstruct compactly supported potentials with only half a derivative in
$L^2$ from the scattering amplitude at a fixed energy. For this we draw a
connection between the recently introduced method of Bukhgeim, which uniquely
determined the potential from the Dirichlet-to-Neumann map, and a question of
Carleson regarding the convergence to initial data of solutions to
time-dependent Schr\"odinger equations. We also provide examples of compactly
supported potentials, with $s$ derivatives in $L^2$ for any $s<1/2$, which
cannot be recovered by these means. Thus the recovery method has a different
threshold in terms of regularity than the corresponding uniqueness result.

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The categories of this paper are: astro-ph
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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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: bayes-an
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The categories of this paper are: physics
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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph