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Proceedings of the American Mathematical Society

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Bounded holomorphic functions in Siegel domains

Author: Su Shing Chen
Journal: Proc. Amer. Math. Soc. 40 (1973), 539-542
MSC: Primary 32H15
MathSciNet review: 0322211
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Abstract: A Siegel domain $ D$ of the second kind (not necessarily affine homogeneous) is shown to be complete with respect to the Carathéodory distance. Thus $ D$ is convex with respect to the bounded holomorphic functions, hence is a domain of holomorphy. A Phragmén-Lindelöf theorem for $ D$ is also given. That is, if a holomorphic function $ f$ in $ D$ is continuous in $ \bar D$, bounded on the distinguished boundary $ S$ of $ D$ and not of exponential growth, then $ f$ is bounded in $ \bar D$.

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Keywords: Siegel domain, convexity with respect to $ B(M)$, Phragmén-Lindelöf theorem, Kobayashi distance, Carathéodory distance, domain of holomorphy, domain of bounded holomorphy
Article copyright: © Copyright 1973 American Mathematical Society