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Algebra i Analiz, 2008, Volume 20, Issue 1, Pages 146–189 (Mi aa501)  

This article is cited in 4 scientific papers (total in 4 papers)

Research Papers

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

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: For a domain $\Omega$ in a complex plane $\mathbb C$, let $H(\Omega)$ denote the space of functions holomorphic in $\Omega$, and let $\mathscr P$ be a family of functions subharmonic in $\Omega$. Denote by $H_{\mathscr P}(\Omega )$ the class of $f\in H(\Omega)$ satisfying $|f(z)|\leq C_f\exp p_f(z)$, $z\in\Omega$, where $p_f \in\mathscr P$ and $C_f$ is a constant. The paper is aimed at conditions for a set $\Lambda\subset\Omega$ to be included in the zero set of some nonzero function in $H_{\mathscr P}(\Omega)$. In the first part, certain preparatory theorems are established about “quenching” the growth of a subharmonic function by adding to it a function of the form $\log|h|$, where $h$ is a nonzero function in $H(\Omega)$. The method is based on the balayage of measures and subharmonic functions.

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

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English version:
St. Petersburg Mathematical Journal, 2009, 20:1, 101–129

Bibliographic databases:

MSC: 30C15
Received: 08.11.2006

Citation: B. N. Khabibullin, F. B. Khabibullin, L. Yu. Cherednikova, “Zero subsequences for classes of holomorphic functions: stability and the entropy of arcwise connectedness. I”, Algebra i Analiz, 20:1 (2008), 146–189; St. Petersburg Math. J., 20:1 (2009), 101–129

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.~I
\jour Algebra i Analiz
\yr 2008
\vol 20
\issue 1
\pages 146--189
\mathnet{http://mi.mathnet.ru/aa501}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2411972}
\zmath{https://zbmath.org/?q=an:1206.30074}
\transl
\jour St. Petersburg Math. J.
\yr 2009
\vol 20
\issue 1
\pages 101--129
\crossref{https://doi.org/10.1090/S1061-0022-08-01040-6}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000267497300006}


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    This publication is cited in the following articles:
    1. 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
    2. B. N. Khabibullin, T. Yu. Baiguskarov, “The Logarithm of the Modulus of a Holomorphic Function as a Minorant for a Subharmonic Function”, Math. Notes, 99:4 (2016), 576–589  mathnet  crossref  crossref  mathscinet  isi  elib
    3. T. Yu. Bayguskarov, G. R. Talipova, B. N. Khabibullin, “Subsequences of zeros for classes of entire functions of exponential type, allocated by restrictions on their growth”, St. Petersburg Math. J., 28:2 (2017), 127–151  mathnet  crossref  mathscinet  isi  elib
    4. B. N. Khabibullin, A. P. Rozit, E. B. Khabibullina, “Poryadkovye versii teoremy Khana—Banakha i ogibayuschie. II. Primeneniya v teorii funktsii”, Kompleksnyi analiz. Matematicheskaya fizika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 162, VINITI RAN, M., 2019, 93–135  mathnet
  • Алгебра и анализ St. Petersburg Mathematical Journal
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