Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Schwarz lemma on the polydisk   There is a known generalization of the classical Schwarz lemma to holomorphic
functions from the polydisk to the disk. In this paper, we characterize those
functions which satisfy equality everywhere in this generalized inequality:
they are the transfer function of an n+1 by n+1 symmetric unitary, and in
particular, are rational, inner, and belong to the Schur-Agler class of the
polydisk. We also present some sufficient conditions for a function to be of
this type.

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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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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: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con