Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A holomorphic map in infinite dimensions   We prove holomorphy E sqcap C(I,varPi) to C(I,varPi) of the map (x,y) mapsto
x circ [id,y] where [id,y]:I owns t mapsto (t,y(t)) for a real compact interval
I, and where varPi is a complex Banach space and E is a certain locally convex
space of continuous functions x:I times varPi to varPi for which x(t,.) is
holomorphic for all t in I. We also discuss application of this result to
establishing a holomorphic solution map (xi,varphi) mapsto y for functions y:I
to varPi satisfying the ordinary differential equation y' = varphi circ [id,y]
with initial condition y(t_0) = xi .

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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: cs
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc