Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global transformations preserving spectral data   We show the existence of a real analytic isomorphism between a space of
impedance function $\rho$ of the Sturm-Liouville problem
  $- \rho^{-2}(\rho^2f')' + uf$ on $(0,1)$, where $u$ is a function of $\rho,
\rho', \rho''$, and that of potential $p$ of the Schr{\"o}dinger equation $-
y'' + py$ on $(0,1)$, keeping their boundary conditions and spectral data.
  This mapping is associated with the classical Liouville transformation $f \to
\rho f$, and yields a global isomorphism between solutions to inverse problems
for the Sturm-Liouville equations of the impedance form and those to the
Schr{\"o}dinger equations.

14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin