Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonlinear conditions for ultradifferentiability   A remarkable theorem of Joris states that a function $f$ is $C^\infty$ if two
relatively prime powers of $f$ are $C^\infty$. Recently, Thilliez showed that
an analogous theorem holds in Denjoy--Carleman classes of Roumieu type. We
prove that a division property, equivalent to Joris's result, is valid in a
wide variety of ultradifferentiable classes. Generally speaking, it holds in
all dimensions for non-quasianalytic classes. In the quasianalytic case we have
general validity in dimension one, but we also get validity in all dimensions
for certain quasianalytic classes.

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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: cs
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int