On the linearity of origin-preserving automorphisms of quasi-circular domains in $\mathbb C^n$

• DOI: 10.48550/arxiv.1404.0309
• Publication Date: 2014-01-01
• Authors: Atsushi Yamamori
• Keywords: Assertion; Linearity

A theorem due to Cartan asserts that every origin-preserving automorphism of bounded circular domains with respect the origin is linear. In present paper, by employing theory Bergman's representative domain, we prove under certain circumstances Cartan's assertion remains true for quasi-circular in $\mathbb C^n$. Our main result applied obtain some simple criterions case $n=3$ and Braun-Kaup-Upmeier's our class domains.