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Mat. Sb., 2009, Volume 200, Number 9, Pages 95–126 (Mi msb4505)  

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

The distribution of the zeros of holomorphic functions of moderate growth in the unit disc and the representation of meromorphic functions there

E. G. Kudashevaa, B. N. Khabibullinbc

a Bashkir State Agricultural University
b Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences
c Bashkir State University, Faculty of Mathematics

Abstract: Let $\mathbb D$ be the unit disc in the complex plane $\mathbb C$ and $H$ a class of holomorphic functions in $\mathbb D$ distinguished by a restriction on their growth in a neighbourhood of the boundary of the disc which is stated in terms of weight functions of moderate growth. Some results which describe the sequences of zeros for holomorphic functions in classes $H$ of this type are obtained. The weight functions defining $H$ are not necessarily radial; however the results obtained are new even in the case of radial constraints. Conditions for meromorphic functions in $\mathbb D$ ensuring that they can be represented as a ratio of two functions in $H$ sharing no zeros are investigated.
Bibliography: 28 titles.

Keywords: unit disc, holomorphic function, sequence of zeros, weighed space, representation of a meromorphic function, subharmonic functions, Green's function.
Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm4505

Full text: PDF file (763 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2009, 200:9, 1353–1382

Bibliographic databases:

UDC: 517.547+517.538+517.574
MSC: Primary 30C15; Secondary 30D30, 30H99
Received: 06.01.2008 and 12.05.2009

Citation: E. G. Kudasheva, B. N. Khabibullin, “The distribution of the zeros of holomorphic functions of moderate growth in the unit disc and the representation of meromorphic functions there”, Mat. Sb., 200:9 (2009), 95–126; Sb. Math., 200:9 (2009), 1353–1382

Citation in format AMSBIB
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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. F. B. Khabibullin, “Sequences of zeroes of holomorphic functions in weight spaces in the unit disk”, Russian Math. (Iz. VUZ), 54:3 (2010), 88–90  mathnet  crossref  mathscinet  elib
    2. F. B. Khabibullin, “Ustoichivost (pod)posledovatelnostei nulei dlya klassov golomorfnykh funktsii umerennogo rosta v edinichnom kruge”, Ufimsk. matem. zhurn., 3:3 (2011), 152–163  mathnet  zmath
    3. E. A. Sevast'yanov, “On zeros of functions rapidly growing in generalized Bergman spaces”, Russian Math. (Iz. VUZ), 61:11 (2017), 40–52  mathnet  crossref  isi
    4. B. N. Khabibullin, A. P. Rozit, “On the Distribution of Zero Sets of Holomorphic Functions”, Funct. Anal. Appl., 52:1 (2018), 21–34  mathnet  crossref  crossref  isi  elib
    5. 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
  • Математический сборник Sbornik: Mathematics (from 1967)
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