Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inversion of the attenuated geodesic X-ray transform over functions and
  vector fields on simple surfaces   We derive explicit reconstruction formulas for the attenuated geodesic X-ray
transform over functions and, in the case of non-vanishing attenuation, vector
fields, on a class of simple Riemannian surfaces with boundary. These formulas
partly rely on new explicit approaches to construct continuous right-inverses
for backprojection operators (and, in turn, holomorphic integrating factors),
which were previously unavailable in a systematic form. The reconstruction of
functions is presented in two ways, the latter one being motivated by numerical
considerations and successfully implemented at the end. Constructing the
right-inverses mentioned require that certain Fredholm equations, first
appearing in [Pestov-Uhlmann, IMRN 2004], be invertible. Whether this last
condition reduces the applicability of the overall approach to a strict subset
of simple surfaces remains open at present.

22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg