Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Kernels of Integral Equations Can Be Boundedly Infinitely Differentiable
  on $\mathbb{R}^2$   In this paper, we reduce the general linear integral equation of the third
kind in $L^2(Y,\mu)$, with largely arbitrary kernel and coefficient, to an
equivalent integral equation either of the second kind or of the first kind in
$L^2(\mathbb{R})$, with the kernel being the linear pencil of bounded
infinitely differentiable bi-Carleman kernels expandable in absolutely and
uniformly convergent bilinear series. The reduction is done by using unitary
equivalence transformations.

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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
10
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: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: physics