Geodesic
The class $R$ and finely analytic functions
Sbornik. Mathematics, Tome 209 (2018) no. 8, pp. 1234-1247

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper is concerned with the class ${R}$ of holomorphic functions introduced by Gonchar, and the class $R^0$, which is a special case of the former. A holomorphic function $f$ in a neighbourhood of $0\in\mathbb{C}$ belongs to ${R}^0$, ${f}\in {R^0}$ if it admits rapid rational approximation in some closed ball $\overline{B}(0, r)$, $r > 0$. It is proved that in certain cases functions in the class $R$ are finely analytic in the whole of $\mathbb{C}$. Bibliography: 26 titles.
Keywords: Gonchar class, fine topology, finely analytic function, rational approximation, Hankel determinant. 
@article{SM_2018_209_8_a5,
     author = {A. Sadullaev and Z. Ibragimov},
     title = {The class $R$ and finely analytic functions},
     journal = {Sbornik. Mathematics},
     pages = {1234--1247},
     publisher = {mathdoc},
     volume = {209},
     number = {8},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2018_209_8_a5/}
}
TY  - JOUR
AU  - A. Sadullaev
AU  - Z. Ibragimov
TI  - The class $R$ and finely analytic functions
JO  - Sbornik. Mathematics
PY  - 2018
SP  - 1234
EP  - 1247
VL  - 209
IS  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2018_209_8_a5/
LA  - en
ID  - SM_2018_209_8_a5
ER  - 
%0 Journal Article
%A A. Sadullaev
%A Z. Ibragimov
%T The class $R$ and finely analytic functions
%J Sbornik. Mathematics
%D 2018
%P 1234-1247
%V 209
%N 8
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2018_209_8_a5/
%G en
%F SM_2018_209_8_a5
A. Sadullaev; Z. Ibragimov. The class $R$ and finely analytic functions. Sbornik. Mathematics, Tome 209 (2018) no. 8, pp. 1234-1247. http://geodesic.mathdoc.fr/item/SM_2018_209_8_a5/