The magic functions and automorphisms of a domain
J. Agler, N. J. Young
TL;DR
This paper introduces the concept of magic functions for complex domains, characterizes them for the symmetrised bidisc, and derives automorphisms and distance formulas, advancing understanding of complex geometric structures.
Contribution
It defines magic functions as intrinsic geometric objects and explicitly determines them for the symmetrised bidisc, including automorphisms and distance formulas.
Findings
Set of magic functions for the symmetrised bidisc determined
Automorphisms of the symmetrised bidisc characterized
Caratheodory distance formula derived for the domain
Abstract
We introduce the notion of magic functions of a general domain in d-dimensional complex space and show that the set of magic functions of a given domain is an intrinsic complex-geometric object. We determine the set of magic functions of the symmetrised bidisc G, and thereby find all automorphisms of G and a formula for the Caratheodory distance on G.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Meromorphic and Entire Functions · advanced mathematical theories