Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Application of approximation theory by nonlinear manifolds in
  Sturm-Liouville inverse problems   We give here some negative results in Sturm-Liouville inverse theory, meaning
that we cannot approach any of the potentials with $m+1$ integrable derivatives
on $\mathbb{R}^+$ by an $\omega$-parametric analytic family better than order
of $(\omega\ln\omega)^{-(m+1)}$.
  Next, we prove an estimation of the eigenvalues and characteristic values of
a Sturm-Liouville operator and some properties of the solution of a certain
integral equation. This allows us to deduce from [Henkin-Novikova] some
positive results about the best reconstruction formula by giving an almost
optimal formula of order of $\omega^{-m}$.

15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph