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Funktsional'nyi Analiz i ego Prilozheniya, 2018, Volume 52, Issue 1, Pages 26–42
DOI: https://doi.org/10.4213/faa3485
(Mi faa3485)
 

This article is cited in 23 scientific papers (total in 23 papers)

On the Distribution of Zero Sets of Holomorphic Functions

B. N. Khabibullin, A. P. Rozit

Bashkir State University, Ufa, Russia
References:
Abstract: Let $M$ be a subharmonic function with Riesz measure $\nu_M$ in a domain $D$ in the $n$-dimensional complex Euclidean space $\mathbb C^n$, and let $f$ be a nonzero function that is holomorphic in $D$, vanishes on a set ${\mathsf Z}\subset D$, and satisfies $|f|\le \exp M$ on $D$. Then restrictions on the growth of $\nu_M$ near the boundary of $D$ imply certain restrictions on the dimensions or the area/volume of $\mathsf Z$. We give a quantitative study of this phenomenon in the subharmonic framework.
Keywords: holomorphic function, zero set, subharmonic function, Riesz measure, Jensen measure.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00024
The work is supported by the Russian Foundation for Basic Research (grant no. 16-01-00024).
Received: 13.11.2016
Revised: 15.09.2017
Accepted: 18.09.2017
English version:
Functional Analysis and Its Applications, 2018, Volume 52, Issue 1, Pages 21–34
DOI: https://doi.org/10.1007/s10688-018-0203-x
Bibliographic databases:
Document Type: Article
UDC: 517.55+517.574+517.987.1
Language: Russian
Citation: B. N. Khabibullin, A. P. Rozit, “On the Distribution of Zero Sets of Holomorphic Functions”, Funktsional. Anal. i Prilozhen., 52:1 (2018), 26–42; Funct. Anal. Appl., 52:1 (2018), 21–34
Citation in format AMSBIB
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  • This publication is cited in the following 23 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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