Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: M\"{o}bius deconvolution on the hyperbolic plane with application to
  impedance density estimation   In this paper we consider a novel statistical inverse problem on the
Poincar\'{e}, or Lobachevsky, upper (complex) half plane. Here the Riemannian
structure is hyperbolic and a transitive group action comes from the space of
$2\times2$ real matrices of determinant one via M\"{o}bius transformations. Our
approach is based on a deconvolution technique which relies on the
Helgason--Fourier calculus adapted to this hyperbolic space. This gives a
minimax nonparametric density estimator of a hyperbolic density that is
corrupted by a random M\"{o}bius transform. A motivation for this work comes
from the reconstruction of impedances of capacitors where the above scenario on
the Poincar\'{e} plane exactly describes the physical system that is of
statistical interest.

15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin