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Funktsional. Anal. i Prilozhen., 2018, Volume 52, Issue 1, Pages 26–42 (Mi faa3485)  

This article is cited in 5 scientific papers (total in 5 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.

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).


DOI: https://doi.org/10.4213/faa3485

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English version:
Functional Analysis and Its Applications, 2018, 52:1, 21–34

Bibliographic databases:

UDC: 517.55+517.574+517.987.1
Received: 13.11.2016
Revised: 15.09.2017

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

Citation in format AMSBIB
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\jour Funktsional. Anal. i Prilozhen.
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. B. Menshikova, B. N. Khabibullin, “K raspredeleniyu nulevykh mnozhestv golomorfnykh funktsii. II”, Funkts. analiz i ego pril., 53:1 (2019), 84–87  mathnet  crossref  elib
    2. B. N. Khabibullin, F. B. Khabibullin, “K raspredeleniyu nulevykh mnozhestv golomorfnykh funktsii. III. Teoremy obrascheniya”, Funkts. analiz i ego pril., 53:2 (2019), 42–58  mathnet  crossref  elib
    3. 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  mathscinet
    4. Khabibullin B.N., Khabibullin F.B., “Zeros of Holomorphic Functions in the Unit Ball and Subspherical Functions”, Lobachevskii J. Math., 40:5, 1, SI (2019), 648–659  crossref  isi
    5. B. N. Khabibullin, A. V. Shmeleva, Z. F. Abdullina, “Vymetanie mer i subgarmonicheskikh funktsii na sistemu luchei. II. Vymetaniya konechnogo roda i regulyarnost rosta na odnom luche”, Algebra i analiz, 32:1 (2020), 208–243  mathnet
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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