Analytic continuation, envelopes of holomorphy, and projective and direct limit spaces
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- by Robert Carmignani PDF
- Trans. Amer. Math. Soc. 209 (1975), 237-258 Request permission
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
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Additional Information
- © Copyright 1975 American Mathematical Society
- 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