The magic functions and automorphisms of a domain

2007/09/02 by Jim Agler, N. J. Young, Agler, J. +1 · 1 citation
Mathematics · #32F32 #32F45 #32M05 #46A55 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.0709.0096

openalex publication_date 2007/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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• Models of holomorphic functions on the symmetrized skew bidisc

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