Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Liouville theorem for L\'evy generators   Under mild assumptions, we establish a Liouville theorem for the "Laplace"
equation $Au=0$ associated with the infinitesimal generator $A$ of a L\'evy
process: If $u$ is a weak solution to $Au=0$ which is at most of (suitable)
polynomial growth, then $u$ is a polynomial. As a by-product, we obtain new
regularity estimates for semigroups associated with L\'evy processes.

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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas