A note on partial polynomial functions, in memory of Marek Jarnicki
Peter Pflug
Abstract
We present an extension theorem for a separately holomorphic function which is polynomial/rational in some variables.
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A note on partial polynomial functions, in memory of Marek Jarnicki
Authors
Abstract
We present an extension theorem for a separately holomorphic function which is polynomial/rational in some variables.
Paper Structure
This paper contains 4 theorems, 34 equations.
Key Result
Theorem 1
If $f\in\mathcal{O}_s(\bold X)$, then there exists an $\widehat{f}\in \mathcal{O}(\widehat{\bold X})$For a domain $S\subset\mathbb C^k$ the set of all holomorphic functions on $S$ is as usually denoted by $\mathcal{O}(S)$. with $\widehat{f}|_{\bold X}=f$.
Theorems & Definitions (10)
- Theorem
- Remark 1
- Lemma 1
- proof
- Theorem 2
- proof
- Remark 3
- Theorem 4
- Remark 5
- proof