Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An F. and M. Riesz theorem for planar vector fields   We prove that solutions of the homogeneous equation $Lu=0$, where $L$ is a
locally integrable vector field with smooth coefficients in two variables
possess the F. and M. Riesz property. That is, if $\Omega$ is an open subset of
the plane with smooth boundary, $u\in C^1(\Omega)$ satisfies $Lu=0$ on
$\Omega$, has tempered growth at the boundary, and its weak boundary value is a
measure $\mu$, then $\mu$ is absolutely continuous with respect to Lebesgue
measure on the noncharacteristic portion of $\partial\Omega$.

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The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: cs
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The categories of this paper are: hep-ex
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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: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th