The magic functions and automorphisms of a domain
Abstract
Description
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.
17 pages. This version contains an additional proposition (2.11) and some minor corrections, notably to Propositions 3.6 and 3.7
17 pages. This version contains an additional proposition (2.11) and some minor corrections, notably to Propositions 3.6 and 3.7