On holomorphic continuation of functions along boundary sections

Imomkulov, S. A., and Khujamov, J. U.. "On holomorphic continuation of functions along boundary sections." Mathematica Bohemica 130.3 (2005): 309-322. <http://eudml.org/doc/249606>.

@article{Imomkulov2005,
abstract = {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 $D^\{\prime \}\times \mathbb \{C\}$.},
author = {Imomkulov, S. A., Khujamov, J. U.},
journal = {Mathematica Bohemica},
keywords = {holomorphic function; holomorphic continuation; pluripolar set; pseudoconcave set; Jacobi-Hartogs series; holomorphic function; pluripolar set; pseudoconcave set; Jacobi-Hartogs series},
language = {eng},
number = {3},
pages = {309-322},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On holomorphic continuation of functions along boundary sections},
url = {http://eudml.org/doc/249606},
volume = {130},
year = {2005},
}

TY - JOUR
AU - Imomkulov, S. A.
AU - Khujamov, J. U.
TI - On holomorphic continuation of functions along boundary sections
JO - Mathematica Bohemica
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 130
IS - 3
SP - 309
EP - 322
AB - 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 $D^{\prime }\times \mathbb {C}$.
LA - eng
KW - holomorphic function; holomorphic continuation; pluripolar set; pseudoconcave set; Jacobi-Hartogs series; holomorphic function; pluripolar set; pseudoconcave set; Jacobi-Hartogs series
UR - http://eudml.org/doc/249606
ER -