Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Radon transforms on compact Lie groups   We show that the Radon transform related to closed geodesics is injective on
a Lie group if and only if the connected components are not homeomorphic to
$S^1$ nor to $S^3$. This is true for both smooth functions and distributions.
The key ingredients of the proof are finding totally geodesic tori and
realizing the Radon transform as a family of symmetric operators indexed by
nontrivial homomorphisms from $S^1$.

1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph