Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Indefinite Sturm-Liouville operators $ (\sgn x) (- \frac{d^2}{dx^2}
  +q(x))$ with finite-zone potentials   The indefinite Sturm-Liouville operator $A = (\sgn x)(-d^2/dx^2+q(x))$ is
studied. It is proved that similarity of $A$ to a selfadjoint operator is
equivalent to integral estimates of Cauchy integrals. Also similarity
conditions in terms of Weyl functions are given. For operators with a
finite-zone potential, the components $\Aess$ and $\Adisc$ of $A$ corresponding
to essential and discrete spectrums, respectively, are considered. A criterion
of similarity of $\Aess$ to a selfadjoint operator is given in terms of Weyl
functions for the Sturm-Liouville operator $-d^2/dx^2+q(x)$ with a finite-zone
potential $q$. Jordan structure of the operator $\Adisc$ is described. We
present an example of the operator $A = (\sgn x)(-d^2/dx^2+q(x))$ such that $A$
is nondefinitizable and $A$ is similar to a normal operator.

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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th