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Algebra i Analiz, 2008, Volume 20, Issue 1, Pages 190–236 (Mi aa502)  

This article is cited in 3 scientific papers (total in 3 papers)

Research Papers

Zero subsequences for classes of holomorphic functions: stability and the entropy of arcwise connectedness. II

B. N. Khabibullinab, F. B. Khabibullinab, L. Yu. Cherednikovaab

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

Abstract: Let $\Omega$ be a domain in the complex plane $\mathbb C$, $H(\Omega)$ the space of functions holomorphic in $\Omega$, and $\mathscr P$ a family of functions subharmonic in $\Omega$. Denote by $H_{\mathscr P}(\Omega)$ the class of functions $f\in H(\Omega)$ satisfying $|f(z)|\leq C_f\exp p_f(z)$ for all $z\in\Omega$, where $p_f\in\mathscr P$ and $C_f$ is a constant. Conditions are found ensuring that a sequence $\Lambda=\{\lambda_k\}\subset\Omega$ be a subsequence of zeros for various classes $H_{\mathscr P}(\Omega)$. As a rule, the results and the method are new already when $\Omega=\mathbb D$ is the unit circle and $\mathscr P$ is a system of radial majorants $p(z)=p(|z|)$.
We continue the enumeration of Part I.

Keywords: Holomorphic function, algebra of functions, weighted space, nonuniqueness sequence

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English version:
St. Petersburg Mathematical Journal, 2009, 20:1, 131–162

Bibliographic databases:

MSC: 30C15
Received: 08.12.2006

Citation: B. N. Khabibullin, F. B. Khabibullin, L. Yu. Cherednikova, “Zero subsequences for classes of holomorphic functions: stability and the entropy of arcwise connectedness. II”, Algebra i Analiz, 20:1 (2008), 190–236; St. Petersburg Math. J., 20:1 (2009), 131–162

Citation in format AMSBIB
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\by B.~N.~Khabibullin, F.~B.~Khabibullin, L.~Yu.~Cherednikova
\paper Zero subsequences for classes of holomorphic functions: stability and the entropy of arcwise connectedness.~II
\jour Algebra i Analiz
\yr 2008
\vol 20
\issue 1
\pages 190--236
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\zmath{https://zbmath.org/?q=an:1206.30075}
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\transl
\jour St. Petersburg Math. J.
\yr 2009
\vol 20
\issue 1
\pages 131--162
\crossref{https://doi.org/10.1090/S1061-0022-08-01041-8}
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    This publication is cited in the following articles:
    1. E. G. Kudasheva, B. N. Khabibullin, “The distribution of the zeros of holomorphic functions of moderate growth in the unit disc and the representation of meromorphic functions there”, Sb. Math., 200:9 (2009), 1353–1382  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. F. B. Khabibullin, “Sequences of zeroes of holomorphic functions in weight spaces in the unit disk”, Russian Math. (Iz. VUZ), 54:3 (2010), 88–90  mathnet  crossref  mathscinet  elib
    3. F. B. Khabibullin, “Ustoichivost (pod)posledovatelnostei nulei dlya klassov golomorfnykh funktsii umerennogo rosta v edinichnom kruge”, Ufimsk. matem. zhurn., 3:3 (2011), 152–163  mathnet  zmath
  • Алгебра и анализ St. Petersburg Mathematical Journal
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