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

Volume 71 / 1999

Do Thai, Dinh Hoang Annales Polonici Mathematici 71 (1999), 105 DOI: 10.4064/ap-71-2-105

Abstract

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 $π_1 : V → Γ$ is finite and proper, then $R_V : O(Γ × G) → Im R_V ⊂ O(V)$ has a right inverse

Authors

  • Do Thai
  • Dinh Hoang

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