Video library: A. Sadullaev, Z. Sh. Ibragimov, Class $R$ of Gonchar and finely-analytic functions

VIDEO LIBRARY


International Conference on Complex Analysis Dedicated to the memory of Andrei Gonchar and Anatoliy Vitushkin October 11, 2016 16:30, Moscow, Steklov Mathematical Institute, Conference hall, 9th floor

Class $R$ of Gonchar and finely-analytic functions A. Sadullaev^ab, Z. Sh. Ibragimov^c ^a Lomonosov Moscow State University ^b National University of Uzbekistan named after Mirzo Ulugbek, ^c Urgench State University named after Al-Khorezmi
Abstract: 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 $\mathbb C^n$. ^* conference room 9th floor