Bounded Holomorphic Functions of Several Complex Variables. I

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1971Publisher:JSTORJournal:Transactions of the American Mathematical Society, volume 158, page 437 (issn: 0002-9947,

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Authors: Kim, Dong Sie;

doi: 10.2307/1995915 , 10.1090/s0002-9947-1971-0280736-2

Bounded Holomorphic Functions of Several Complex Variables. I

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Abstract

A domain of bounded holomorphy in a complex analytic manifold is a maximal domain for which every bounded holomorphic function has a bounded analytic continuation. In this paper, we show that this is a local property: if, for each boundary point of a domain, there exists a bounded holomorphic function which cannot be continued to any neighborhood of the point, then there exists a single bounded holomorphic function which cannot be continued to any neighborhood of the boundary points.

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Tulane University
United States

Keywords

complex functions

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