Abstract.
We introduce the notion of magic functions of a general domain in \({\mathbb{C}}^d\) 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 Carathéodory distance on G.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Daniel Alpay.
Submitted: August 31, 2007. Accepted: November 11, 2007.
Rights and permissions
About this article
Cite this article
Agler, J., Young, N.J. The Magic Functions and Automorphisms of a Domain. Complex anal.oper. theory 2, 383–404 (2008). https://doi.org/10.1007/s11785-007-0039-5
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11785-007-0039-5