Algebra i Analiz
 RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Subscription Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

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

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

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

Full text: PDF file (533 kB)
References: PDF file   HTML file

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

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. I”, Algebra i Analiz, 20:1 (2008), 146–189; St. Petersburg Math. J., 20:1 (2009), 101–129

Citation in format AMSBIB
\Bibitem{KhaKhaChe08} \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} 

• http://mi.mathnet.ru/eng/aa501
• http://mi.mathnet.ru/eng/aa/v20/i1/p146

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles
Cycle of papers

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
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
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
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
•  Number of views: This page: 400 Full text: 127 References: 38 First page: 8