Uniqueness property for quasiharmonic functions

In this paper we consider class of continuous functions, called quasiaharmonic functions, admitting best approximations by harmonic polynomials. In this class we prove a uniqueness theorem by analogy with the analytic functions

Pluripolarity of Graphs of Denjoy Quasianalytic Functions of Several Variables

In this paper we prove pluripolarity of graphs of Denjoy quasianalytic functions of several variables on the spanning se

On holomorphic continuation of functions along boundary sections

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 $D^{\prime }\times \mathbb{C}$