Geodesic
The class $R$ and finely analytic functions
Sbornik. Mathematics, Tome 209 (2018) no. 8, pp. 1234-1247 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

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