Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Analytic continuation, envelopes of holomorphy, and projective and direct limit spaces


Author: Robert Carmignani
Journal: Trans. Amer. Math. Soc. 209 (1975), 237-258
MSC: Primary 32D10
DOI: https://doi.org/10.1090/S0002-9947-1975-0385165-2
MathSciNet review: 0385165
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For a Riemann domain $ \Omega $, a connected complex manifold where $ n(n = dimension)$ globally defined functions form a local system of coordinates at every point, and an arbitrary holomorphic function $ f$ in $ \Omega $, the ``Riemann surface'' $ {\Omega _f}$, a maximal holomorphic extension Riemann domain for $ f$, is formed from the direct limit of a sequence of Riemann domains. Projective limits are used to construct an envelope of holomorphy for $ \Omega $, a maximal holomorphic extension Riemann domain for all holomorphic functions in $ \Omega $, which is shown to be the projective limit space of the ``Riemann surfaces'' $ {\Omega _f}$. Then it is shown that the generalized notion of envelope of holomorphy of an arbitrary subset of a Riemann domain can also be characterized in a natural way as the projective limit space of a family of ``Riemann surfaces".


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 32D10

Retrieve articles in all journals with MSC: 32D10


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1975-0385165-2
Keywords: Riemann domain, direct limit space, domain of holomorphy, projective limit, projective limit spaces, envelope of holomorphy, Stein manifold, holomorphically convex sets, convex hull
Article copyright: © Copyright 1975 American Mathematical Society