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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
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.
Received: 13.11.2016 Revised: 15.09.2017 Accepted: 18.09.2017
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
Linking options:
https://www.mathnet.ru/eng/faa3485https://doi.org/10.4213/faa3485 https://www.mathnet.ru/eng/faa/v52/i1/p26
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