Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The higher order fractional Calder\'on problem for linear local
  operators: uniqueness   We study an inverse problem for the fractional Schr\"odinger equation (FSE)
with a local perturbation by a linear partial differential operator (PDO) of
order smaller than the order of the fractional Laplacian. We show that one can
uniquely recover the coefficients of the PDO from the Dirichlet-to-Neumann (DN)
map associated to the perturbed FSE. This is proved for two classes of
coefficients: coefficients which belong to certain spaces of Sobolev
multipliers and coefficients which belong to fractional Sobolev spaces with
bounded derivatives. Our study generalizes recent results for the zeroth and
first order perturbations to higher order perturbations.

19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs