Geodesic
Zero subsets, representation of meromorphic functions, and Nevanlinna characteristics in a~disc
Sbornik. Mathematics, Tome 197 (2006) no. 2, pp. 259-279

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Let $\Lambda=\{\lambda_k\}$ be a point sequence in the unit disc $\mathbb D$ and $N_\Lambda(r)$ the Nevanlinna characteristic of the sequence $\Lambda$, $0$. In terms of the Nevanlinna characteristic $N_\Lambda(r)$ one finds estimates for the slowest possible growth of the characteristic $B(r,|f|)=\max\{|f(z)|:|z|=r\}$ as $r\to1-0$ in the class of holomorphic functions $f\not\equiv0$ in $\mathbb D$ vanishing on $\Lambda$. Let $F$ be a meromorphic function in $\mathbb D$. In terms of the Nevanlinna characteristic function $T(r,F)$ of $F$ one finds estimates for the slowest possible growth of the characteristics $B(r,|g|)$ and $B(r,|h|)$ in the class of pairs of holomorphic functions $g$ and $h$ such that $F=g/h$. Bibliography: 21 titles.
Keywords: holomorphic function, unit disk, zero set, meromorphic function, nonuniqueness set, Nevanlinna characteristic, Jensen measure. 
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     author = {B. N. Khabibullin},
     title = {Zero subsets, representation of meromorphic functions, and {Nevanlinna} characteristics in a~disc},
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B. N. Khabibullin. Zero subsets, representation of meromorphic functions, and Nevanlinna characteristics in a~disc. Sbornik. Mathematics, Tome 197 (2006) no. 2, pp. 259-279. http://geodesic.mathdoc.fr/item/SM_2006_197_2_a7/