Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Recovering of a potential of Sturm-Liouville operator from a finite sets
  of eigenvalues and norming constants   It is well known that a potential $q$ of the Sturm-Liouville operator $Ly=
-y" +q(x)y$ on the finite interval $[0, \pi]$ can be uniquely recovered by the
spectrum $\{\lambda_k\}_1^\infty$ and norming constants $\{\alpha_k\}_1^\infty$
of this operator with Dirichlet boundary conditions. Given potential $q$
belonging to Sobolev space $W^\theta_2[0, \pi]$ with $\theta > -1$ we associate
its $2N$-approximation $q_N$ constructed by the final sets $\{\lambda_k\}_1^N$
and $\{\alpha_k\}_1^N$. The main result claims that for $-1\leqslant\tau
<\theta$ the estimate $\|q -q_N\|_\tau \leqslant CN^{\theta-\tau}$ holds, where
$\|\cdot\|_\tau$ is the norm in $W^\tau_2$ and the constant $C$ depends on $R$
but does not depend on $q$ if $\|q\|_\theta \leqslant R$.

26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th