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 Algebra i Analiz: Year: Volume: Issue: Page: Find

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

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

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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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
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
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
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