Analytic continuation, envelopes of holomorphy, and projective and direct limit spaces
نویسندگان
چکیده
منابع مشابه
Analytic Continuation , Envelopes of Holomorphy , and Projective and Direct Limit Spaces
For a Riemann domain Í2, 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 / in Í2, the "Riemann surface" Slf, a maximal holomorphic extension Riemann domain for /, is formed from the direct limit of a sequence of Riemann domains. Projective limits are used to construct an enve...
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15 صفحه اولAnalytic Continuation in Mapping Spaces
We consider a Stein manifold M of dimension ≥ 2 and a compact subset K ⊂ M such that M ′ = M\K is connected. Let S be a compact differential manifold, and let MS , resp. M ′ S stand for the complex manifold of maps S → M , resp. S → M , of some specified regularity that are homotopic to constant. We prove that any holomorphic function on M ′ S continues analytically to MS (perhaps as a multival...
متن کاملA Schlichtness Theorem for Envelopes of Holomorphy
Let Ω be a domain in C. We prove the following theorem. If the envelope of holomorphy of Ω is schlicht over Ω, then the envelope is in fact schlicht. We provide examples showing that the conclusion of the theorem does not hold in Cn, n > 2. Additionally, we show that the theorem cannot be generalized to provide information about domains in C whose envelopes are multiply sheeted.
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1975
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1975-0385165-2