The magic functions and automorphisms of a domain
Complex Variables
2008-07-15 v2 Functional Analysis
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.
Cite
@article{arxiv.0709.0096,
title = {The magic functions and automorphisms of a domain},
author = {J. Agler and N. J. Young},
journal= {arXiv preprint arXiv:0709.0096},
year = {2008}
}
Comments
17 pages. This version contains an additional proposition (2.11) and some minor corrections, notably to Propositions 3.6 and 3.7