Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A multiplicative product of distributions and a class of ordinary
  differential equations with distributional coefficients   We construct a generalization of the multiplicative product of distributions
presented by L. H\"ormander in [L. H\"ormander, {\it The analysis of linear
partial differential operators I} (Springer-Verlag, 1983)]. The new product is
defined in the vector space ${\mathcal A}(\bkR)$ of piecewise smooth functions
$f: \bkR \to \bkC$ and all their (distributional) derivatives. It is
associative, satisfies the Leibniz rule and reproduces the usual pointwise
product of functions for regular distributions in ${\mathcal A}(\bkR)$. Endowed
with this product, the space ${\mathcal A}(\bkR)$ becomes a differential
associative algebra of generalized functions. By working in the new ${\mathcal
A}(\bkR)$-setting we determine a method for transforming an ordinary linear
differential equation with general solution $\psi$ into another, ordinary
linear differential equation, with general solution $\chi_{\Omega} \psi$, where
$\chi_{\Omega}$ is the characteristic function of some prescribed interval
$\Omega \subset \bkR$.

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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
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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: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: cs
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys