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The class $R$ and finely analytic functions
A. Sadullaeva†, Z. Ibragimovb
a National University of Uzbekistan named after M. Ulugbek, Tashkent, Uzbekistan
b Urgench State University named after Al-Khorezmi, Uzbekistan
Abstract:
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.
† Author to whom correspondence should be addressed
DOI:
https://doi.org/10.4213/sm8846
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English version:
Sbornik: Mathematics, 2018, 209:8, 1234–1247
Bibliographic databases:
   
UDC:
517.518.84+517.547.22+517.55
MSC: Primary 30G12, 41A20; Secondary 30E10
Received: 17.10.2016 and 14.03.2018
Citation:
A. Sadullaev, Z. Ibragimov, “The class $R$ and finely analytic functions”, Mat. Sb., 209:8 (2018), 138–151; Sb. Math., 209:8 (2018), 1234–1247
Citation in format AMSBIB
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http://mi.mathnet.ru/eng/msb8846https://doi.org/10.4213/sm8846 http://mi.mathnet.ru/eng/msb/v209/i8/p138
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