Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reconstruction formulas for X-ray transforms in negative curvature   We give reconstruction formulas inverting the geodesic X-ray transform over
functions (call it $I_0$) and solenoidal vector fields on surfaces with
negative curvature and strictly convex boundary. These formulas generalize the
Pestov-Uhlmann formulas in [Pestov-Uhlmann, IMRN '04] (established for simple
surfaces) to cases allowing geodesics with infinite length on surfaces with
trapping. Such formulas take the form of Fredholm equations, where the analysis
of error operators requires deriving new estimates for the normal operator
$\Pi_0 = I_0^* I_0$. Numerical examples are provided at the end.

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The categories of this paper are: quant-ph
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
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The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
1
The categories of this paper are: cs
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: q-alg