Abstract
According to S. Bochner [6, 7]: IfD =B +iℝn is a tube domain in ℂn, where B is a domain in ℝn, and if\(\tilde B\) is the convex envelope of B, then any holomorphic function on D extends to the tube domain\(\tilde D = \tilde B + i\mathbb{R}^n \), which is a univalent envelope of holomorphy of D. We give a generalization of this result to (nonunivalent) tube domains over a complex Lie group which admit a closed sub-group as a real form. Application: If (V, φ) is a tube domain over ℂn and if B is the convex envelope of ϕ(V)∩ℝn in ℝn, then\(\tilde V = B + i\mathbb{R}^n \) is an envelope of holomorphy of (V, φ).
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Sahraoui, F. Envelope of holomorphy of a tube domain over a complex Lie group. J Geom Anal 16, 167–185 (2006). https://doi.org/10.1007/BF02930991
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DOI: https://doi.org/10.1007/BF02930991