Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Operator monotone functions and L\"owner functions of several variables   We prove generalizations of L\"owner's results on matrix monotone functions
to several variables. We give a characterization of when a function of $d$
variables is locally monotone on $d$-tuples of commuting self-adjoint
$n$-by-$n$ matrices. We prove a generalization to several variables of
Nevanlinna's theorem describing analytic functions that map the upper
half-plane to itself and satisfy a growth condition. We use this to
characterize all rational functions of two variables that are operator
monotone.

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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
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The categories of this paper are: nlin
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ph
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The categories of this paper are: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas