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An extension of H. Cartan's theorem |
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| Authors: | So-chin Chen Shih-Biau Jang |
| Affiliation: | Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan, Republic of China Shih-Biau Jang ; Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan, Republic of China |
| Abstract: | In this article we prove that if  ,  , is a bounded pseudoconvex domain with real analytic boundary, then for each  , there exists a fixed open neighborhood  of  and an open neighborhood  of  in  such that any  can be extended holomorphically to  , and that the action defined by
is real analytic in joint variables. This extends H. Cartan's theorem beyond the boundary. Some applications are also discussed here. |
| Keywords: | Automorphism group pseudoconvex domains condition $R$ |
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