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Continuous linear extension operators on spaces of holomorphic functions on closed subgroups of a complex Lie group

Do Duc Thai; Dinh Huy Hoang — 1999

Annales Polonici Mathematici

We show that the restriction operator of the space of holomorphic functions on a complex Lie group to an analytic subset V has a continuous linear right inverse if it is surjective and if V is a finite branched cover over a connected closed subgroup Γ of G. Moreover, we show that if Γ and G are complex Lie groups and V ⊂ Γ × G is an analytic set such that the canonical projection $π_{1} : V \to Γ$ is finite and proper, then $R_{V} : O (Γ \times G) \to I m R_{V} \subset O (V)$ has a right inverse

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