| Title:
|
On holomorphic continuation of functions along boundary sections (English) |
| Author:
|
Imomkulov, S. A. |
| Author:
|
Khujamov, J. U. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
130 |
| Issue:
|
3 |
| Year:
|
2005 |
| Pages:
|
309-322 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $D^{\prime } \subset \mathbb{C}^{n-1}$ be a bounded domain of Lyapunov and $f(z^{\prime },z_n)$ a holomorphic function in the cylinder $D=D^{\prime }\times U_n$ and continuous on $\bar{D}$. If for each fixed $a^{\prime }$ in some set $E\subset \partial D^{\prime }$, with positive Lebesgue measure $\text{mes}\,E>0$, the function $f(a^{\prime },z_n)$ of $z_n$ can be continued to a function holomorphic on the whole plane with the exception of some finite number (polar set) of singularities, then $f(z^{\prime },z_n)$ can be holomorphically continued to $(D^{\prime }\times \mathbb{C})\setminus S$, where $S$ is some analytic (closed pluripolar) subset of $D^{\prime }\times \mathbb{C}$. (English) |
| Keyword:
|
holomorphic function |
| Keyword:
|
holomorphic continuation |
| Keyword:
|
pluripolar set |
| Keyword:
|
pseudoconcave set |
| Keyword:
|
Jacobi-Hartogs series |
| MSC:
|
32D15 |
| MSC:
|
46G20 |
| idZBL:
|
Zbl 1113.46038 |
| idMR:
|
MR2164660 |
| DOI:
|
10.21136/MB.2005.134101 |
| . |
| Date available:
|
2009-09-24T22:21:35Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134101 |
| . |
| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
