Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An application of the fixed point theorem to the inverse Sturm-Liouville
  problem   We consider Sturm-Liouville operators $-y''+v(x)y$ on $[0,1]$ with Dirichlet
boundary conditions $y(0)=y(1)=0$. For any $1\le p<\infty$, we give a short
proof of the characterization theorem for the spectral data corresponding to
$v\in L^p(0,1)$.

6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg