Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The (strong) Liouville property for a class of non-local operators   We prove a necessary and sufficient condition for the Liouville and strong
Liouville properties of the infinitesimal generator of a L\'evy process and
subordinate L\'evy processes. Combining our criterion with the necessary and
sufficient condition obtained by Alibaud et al., we obtain a characterization
of (orthogonal subgroup of) the set of zeros of the characteristic exponent of
the L\'evy process.

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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci