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On Holomorphic Extension from the Boundary
| Content Provider | Scilit |
|---|---|
| Author | Shiga, Kiyoshi |
| Copyright Year | 1971 |
| Description | Let D be a bounded domain of the complex n-space $C^{n}$(n≥2), or more generally a pair (M,D) a finite manifold (cf. Definition 2.1), and we assume the boundary ∂D is a smooth and connected submanifold. It is well known by Hartogs-Osgood’s theorem that every holomorphic function on a neighbourhood of ∂D can be continued holomorphically to D. Generalizing the above theorem we shall prove that if a differentiable function on ∂D satisfies certain conditions which are satisfied for the trace of a holomorphic function on a neighbourhood of ∂D, then it can be continued holomorphically to D (Theorem 2-5). The above conditions will be called the tangential Cauchy Riemann equations. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/E419332C5476A99BB74DF46A610BC40A/S0027763000014239a.pdf/div-class-title-on-holomorphic-extension-from-the-boundary-div.pdf |
| Ending Page | 66 |
| Page Count | 10 |
| Starting Page | 57 |
| ISSN | 00277630 |
| e-ISSN | 21526842 |
| DOI | 10.1017/s0027763000014239 |
| Journal | Nagoya Mathematical Journal |
| Volume Number | 42 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 1971-03-01 |
| Access Restriction | Open |
| Subject Keyword | Nagoya Mathematical Journal Mathematical Physics |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
