Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An inverse problem for self-adjoint positive Hankel operators   For a sequence $\{\alpha_n\}_{n=0}^\infty$, we consider the Hankel operator
$\Gamma_\alpha$, realised as the infinite matrix in $\ell^2$ with the entries
$\alpha_{n+m}$. We consider the subclass of such Hankel operators defined by
the "double positivity" condition $\Gamma_\alpha\geq0$,
$\Gamma_{S^*\alpha}\geq0$; here $S^*\alpha$ is the shifted sequence
$\{\alpha_{n+1}\}_{n=0}^\infty$. We prove that in this class, the sequence
$\alpha$ is uniquely determined by the spectral shift function $\xi_\alpha$ for
the pair $\Gamma_\alpha^2$, $\Gamma_{S^*\alpha}^2$. We also describe the class
of all functions $\xi_\alpha$ arising in this way and prove that the map
$\alpha\mapsto\xi_\alpha$ is a homeomorphism in appropriate topologies.

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The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
3
The categories of this paper are: physics
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The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
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The categories of this paper are: comp-gas