On the linearity of origin-preserving automorphisms of quasi-circular domains in Cn
On the linearity of origin-preserving automorphisms of quasi-circular domains in Cn
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DOI：
10.1016/j.jmaa.2015.01.061
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发表时间：
2015-06
影响因子：
1.3
通讯作者：
Atsushi Yamamori
中科院分区：
文献类型：
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作者：
Atsushi Yamamori
嘉当的一个定理断言，有界圆域关于原点的保原点自同构是线性的。本文利用Bergman的代表域理论，证明了在一定条件下，Cartan的结论对Cn中的拟圆域仍然成立.我们的主要结果被应用于获得一些简单的准则的情况下n= 3，并证明Braun-Kaup-Upmeier定理仍然适用于我们的类准圆域。
A theorem due to Cartan asserts that every origin-preserving automorphism of bounded circular domains with respect to the origin is linear. In the present paper, by employing the theory of Bergman's representative domain, we prove that under certain circumstances Cartan's assertion remains true for quasi-circular domains in C n. Our main result is applied to obtain some simple criterions for the case n= 3 and to prove that Braun–Kaup–Upmeier's theorem remains true for our class of quasi-circular domains.