Class $R$ of Gonchar and finely-analytic functions

In this talk we consider the class $R$ of germs of holomorphic functions, introduced by A. Gonchar. A germ of analytic function $f$ at the point $o\in\mathbb C^n$ belongs to the class $R$ if for some closed neighborhood $\overline{B}(o,r)$, $r>0$, it admits rapid rational approximation. It is proved that in some cases, the functions of this class will be finely-analytic in the whole space $\mathbb C^n$.