Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invariant subspaces of a generalized backward shift operator and
  rational functions   We obtaine the full characterization of proper closed invariant subspaces of
a generalized backward shift operator (Pommiez operator) in the Frechet space
of all holomorphic functions on a simply connected domain $\Omega$ of the
complex plane, containing the origin. In the case when the function, which
defines this operator, is not has zeros in $\Omega$ all such subspaces are
finite-dimensional. If additionally $\Omega $ coincides with the complex plane,
then the considered operator is unicellular. If this function has zeros in
$\Omega $, then the family of mentioned invariant subspaces splits into two
classes: the first consists of finite-dimensional subspaces, and the second of
infinite-dimensional ones.

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The categories of this paper are: nlin
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th