| Title:
|
A pure smoothness condition for Radó's theorem for $\alpha $-analytic functions (English) |
| Author:
|
Daghighi, Abtin |
| Author:
|
Wikström, Frank |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
66 |
| Issue:
|
1 |
| Year:
|
2016 |
| Pages:
|
57-62 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $\Omega \subset \mathbb {C}^n$ be a bounded, simply connected $\mathbb C$-convex domain. Let $\alpha \in \mathbb Z_+^n$ and let $f$ be a function on $\Omega $ which is separately $C^{2\alpha _j-1}$-smooth with respect to $z_j$ (by which we mean jointly $C^{2 \alpha _j-1}$-smooth with respect to $\mathop {\rm Re} z_j$, $ \mathop {\rm Im} z_j$). If $f$ is $\alpha $-analytic on $\Omega \setminus f^{-1}(0)$, then $f$ is $\alpha $-analytic on $\Omega $. The result is well-known for the case $\alpha _i=1$, $1\leq i\leq n$, even when $f$ a priori is only known to be continuous. (English) |
| Keyword:
|
$\alpha $-analytic function |
| Keyword:
|
polyanalytic function |
| Keyword:
|
zero set |
| Keyword:
|
Radó's theorem |
| MSC:
|
30C15 |
| MSC:
|
32A99 |
| MSC:
|
32U15 |
| MSC:
|
35G05 |
| idZBL:
|
Zbl 06587872 |
| idMR:
|
MR3483221 |
| DOI:
|
10.1007/s10587-016-0238-1 |
| . |
| Date available:
|
2016-04-07T14:52:27Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144876 |
| . |
| Reference:
|
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| Reference:
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| . |
