Domains of existence of slice regular functions in one quaternionic variable
arxiv(2024)
摘要
Recently, we introduced domains of slice regularity in the space ℍ
of quaternions and also proved that domains of slice regularity satisfy a
symmetry with respect to paths, called 2-path-symmetry. In this paper, we
give a full characterization by showing that all 2-path-symmetric slice-open
sets are domains of slice regularity. In fact, we will prove a counterpart of
the Cartan-Thullen theorem for slice regular functions, namely that a
slice-open set is a domain of existence for some slice regular function if and
only if it is a domain of slice regularity, if and only if it is
slice-regularly convex, if and only if it is 2-path-symmetric. As a tool, we
also prove an interpolation theorem of independent interest.
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