Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Overdetermined Transforms in Integral Geometry   A simple example of an $n$-dimensional admissible complex of planes is given
for the overdetermined $k$-plane transform in $\mathbb{R}^n$. For the
corresponding restricted $k$-plane transform sharp existence conditions are
obtained and explicit inversion formulas are discussed in the general context
of $L^p$ functions. Similar questions are studied for overdetermined Radon type
transforms on the sphere and the hyperbolic space. A theorem describing the
range of the restricted $k$-plane transform on the space of rapidly decreasing
smooth functions is proved.

28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
18
The categories of this paper are: econ
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph