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Analytic Continuation, Envelopes of Holomorphy, and Projective and Direct Limit Spaces
| Content Provider | Scilit |
|---|---|
| Author | Carmignani, Robert |
| Copyright Year | 1975 |
| Description | For a Riemann domain , a connected complex manifold where globally defined functions form a local system of coordinates at every point, and an arbitrary holomorphic function in , the ``Riemann surface'' , 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 envelope of holomorphy for , a maximal holomorphic extension Riemann domain for all holomorphic functions in , which is shown to be the projective limit space of the ``Riemann surfaces'' . 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". |
| Related Links | http://www.ams.org/tran/1975-209-00/S0002-9947-1975-0385165-2/S0002-9947-1975-0385165-2.pdf |
| Ending Page | 258 |
| Page Count | 22 |
| Starting Page | 237 |
| ISSN | 00029947 |
| e-ISSN | 10886850 |
| DOI | 10.2307/1997382 |
| Journal | Transactions of the American Mathematical Society |
| Volume Number | 209 |
| Language | English |
| Publisher | Duke University Press |
| Access Restriction | Open |
| Subject Keyword | Mathematical Physics Analytic Continuation Holomorphy Direct Limit Limit Spaces Projective Envelopes |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics |
