Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A spectral Szego theorem on the real line   We characterize even measures $\mu=wdx+\mu_s$ on the real line with finite
entropy integral $\int_{R} \frac{\log w(t)}{1+t^2}dt>-\infty$ in terms of
$2\times 2$ Hamiltonian generated by $\mu$ in the sense of inverse spectral
theory. As a corollary, we obtain criterion for spectral measure of Krein
string to have converging logarithmic integral.

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The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys