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This article is cited in 5 scientific papers (total in 5 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.
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
Linking options:
https://www.mathnet.ru/eng/aa502 https://www.mathnet.ru/eng/aa/v20/i1/p190
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Abstract page: | 533 | Full-text PDF : | 148 | References: | 82 | First page: | 5 |
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