S. A. Imomkulov, J. U. Khujamov, Urganch State University, Urganch city, Khamid Alimjan-14, 740 000, Uzbekistan
Abstract: Let $D' \subset\Bbb C^{n-1}$ be a bounded domain of Lyapunov and $f(z',z_n)$ a holomorphic function in the cylinder $D=D'\times U_n$ and continuous on $\bar{D}$. If for each fixed $a'$ in some set $E\subset\partial D'$, with positive Lebesgue measure $\text{mes} E>0$, the function $f(a',z_n)$ 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 $f(z',z_n)$ can be holomorphically continued to $(D'\times\Bbb C)\setminus S$, where $S$ is some analytic (closed pluripolar) subset of $D'\times\Bbb C$.
Keywords: holomorphic function, holomorphic continuation, pluripolar set, pseudoconcave set, Jacobi-Hartogs series
Classification (MSC2000): 46G20
Full text of the article: