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AN EXTENSION OF H. CARTAN’S THEOREM SO-CHIN CHEN AND SHIH-BIAU JANG

By Communicated Steven R. Bell

Abstract

Abstract. In this article we prove that if D ⊂ Cn, n ≥ 2, is a bounded pseudoconvex domain with real analytic boundary, then for each g(z) ∈ Aut(D), there exists a fixed open neighborhood Ωg of D andanopenneighborhoodVg of g(z) inAut(D) such that any h(z) ∈ Vg can be extended holomorphically to Ωg, and that the action defined by π:Vg × Ωg → C n (f, z) ↦ → π(f, z) =f(z) is real analytic in joint variables. This extends H. Cartan’s theorem beyond the boundary. Some applications are also discussed here. 1

Year: 2013
OAI identifier: oai:CiteSeerX.psu:10.1.1.352.3818
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