Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Covering results and perturbed Roper--Suffridge operators   This work is devoted to the advanced study of Roper--Suffridge type extension
operators. For a given non-normalized spirallike function (with respect to an
interior or boundary point) on the open unit disk of the complex plane, we
construct perturbed extension operators in a certain class of Banach spaces and
prove that these operators preserve the spirallikeness property. In addition,
we present an extension operator for semigroup generators.
  We use a new geometric approach based on the connection between spirallike
mappings and one-parameter continuous semigroups. It turns out that the new
one-dimensional covering results established below are crucial for our
investigation.

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The categories of this paper are: econ
6
The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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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: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph