Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Representing kernels of perturbations of Toeplitz operators by backward
  shift-invariant subspaces   It is well known that the kernel of a Toeplitz operator is nearly invariant
under the backward shift $S^*$. This paper shows that kernels of finite-rank
perturbations of Toeplitz operators are nearly $S^*$-invariant with finite
defect. This enables us to apply a recent theorem by
Chalendar--Gallardo--Partington to represent the kernel in terms of backward
shift-invariant subspaces, which we identify in several important cases.

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The categories of this paper are: patt-sol
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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: stat
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex