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Mat. Sb., 2006, Volume 197, Number 2, Pages 117–136 (Mi msb1510)  

This article is cited in 2 scientific papers (total in 2 papers)

Zero subsets, representation of meromorphic functions, and Nevanlinna characteristics in a disc

B. N. Khabibullinab

a Bashkir State University
b Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences

Abstract: Let $\Lambda=\{\lambda_k\}$ be a point sequence in the unit disc $\mathbb D$ and $N_\Lambda(r)$ the Nevanlinna characteristic of the sequence $\Lambda$, $0<r<1$. 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

DOI: https://doi.org/10.4213/sm1510

Full text: PDF file (644 kB)
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English version:
Sbornik: Mathematics, 2006, 197:2, 259–279

Bibliographic databases:

UDC: 517.53+517.547+517.574
MSC: 30D30
Received: 24.05.2004 and 21.11.2005

Citation: B. N. Khabibullin, “Zero subsets, representation of meromorphic functions, and Nevanlinna characteristics in a disc”, Mat. Sb., 197:2 (2006), 117–136; Sb. Math., 197:2 (2006), 259–279

Citation in format AMSBIB
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\by B.~N.~Khabibullin
\paper Zero subsets, representation of meromorphic functions, and Nevanlinna characteristics in a~disc
\jour Mat. Sb.
\yr 2006
\vol 197
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\pages 117--136
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\crossref{https://doi.org/10.4213/sm1510}
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\elib{http://elibrary.ru/item.asp?id=9200275}
\transl
\jour Sb. Math.
\yr 2006
\vol 197
\issue 2
\pages 259--279
\crossref{https://doi.org/10.1070/SM2006v197n02ABEH003757}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. B. N. Khabibullin, “Zero sequences of holomorphic functions, representation of meromorphic functions, and harmonic minorants”, Sb. Math., 198:2 (2007), 261–298  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. B. N. Khabibullin, F. B. Khabibullin, L. Yu. Cherednikova, “Zero subsequences for classes of holomorphic functions: stability and the entropy of arcwise connectedness. II”, St. Petersburg Math. J., 20:1 (2009), 131–162  mathnet  crossref  mathscinet  zmath  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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