Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Eigenfunctions of Composition Operators on Bloch-type Spaces   Suppose $\varphi$ is a holomorphic self map of the unit disk and $C_\varphi$
is a composition operator with symbol $\varphi$ that fixes the origin and
$0<|\varphi'(0)|<1$. This work explores sufficient conditions that ensure all
holomorphic solutions of Schr\"oder equation for the composition operator
$C_\varphi$ belong to a Bloch-type space $\mathcal{B}_\alpha$ for some
$\alpha>0$. The results from composition operators have been extended to
weighted composition operators in the second part of this work.

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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
3
The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: cs
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The categories of this paper are: hep-th
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph