NDLI: Envelopes of Holomorphy and Holomorphic Convexity

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Envelopes of Holomorphy and Holomorphic Convexity

Content Provider	Scilit
Author	Carmignani, Robert
Copyright Year	1973
Description	This paper is primarily a study of generalized notions of envelope of holomorphy and holomorphic convexity for special (algebraically restricted) subsets of and in part for arbitrary subsets of . For any special set S in , we show that every function holomorphic in a neighborhood of S not only can be holomorphically continued but also holomorphically extended to a neighborhood in of a maximal set , the ``envelope of holomorphy'' of S, which is also a special set of the same type as S. Formulas are obtained for constructing for any special set S. ``Holomorphic convexity'' is characterized for these special sets. With one exception, the only topological restriction on these special sets is connectivity. Examples are given which illustrate applications of the theorems and help to clarify the concepts of ``envelope of holomorphy'' and ``holomorphic convexity."
Related Links	http://www.ams.org/tran/1973-179-00/S0002-9947-1973-0316748-1/S0002-9947-1973-0316748-1.pdf
Ending Page	431
Page Count	17
Starting Page	415
ISSN	00029947
e-ISSN	10886850
DOI	10.2307/1996512
Journal	Transactions of the American Mathematical Society
Volume Number	179
Language	English
Publisher	Duke University Press
Access Restriction	Open
Subject Keyword	Logic Spread Stein Manifold Projective Limit Strictly Convex Logarithmically Convex Spectrum Domain of Holomorphy
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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