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Mat. Sb., 2007, Volume 198, Number 2, Pages 121–160 (Mi msb1318)  

This article is cited in 6 scientific papers (total in 6 papers)

Zero sequences of holomorphic functions, representation of meromorphic functions, and harmonic minorants

B. N. Khabibullinab

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

Abstract: Let $\Lambda=\{\lambda_k\}$ be a point sequence in a subdomain $\Omega$ of the complex plane $\mathbb C$. In terms of harmonic measures, Green's functions, balayage, Jensen measures, and so on, general conditions are described ensuring that $\Lambda$ is the zero sequence of a holomorphic function in a prescribed weighted space of holomorphic functions in $\Omega$. The question of the representation of a meromorphic function in $\Omega$ as the ratio of holomorphic functions without common zeros from a prescribed weighted space is considered in similar terms. Some applications are presented.
Bibliography: 46 titles.

DOI: https://doi.org/10.4213/sm1318

Full text: PDF file (895 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2007, 198:2, 261–298

Bibliographic databases:

UDC: 517.53+517.54+517.57+517.98
MSC: Primary 30C15, 30D30; Secondary 31A05, 31A15
Received: 18.10.2005 and 30.10.2006

Citation: B. N. Khabibullin, “Zero sequences of holomorphic functions, representation of meromorphic functions, and harmonic minorants”, Mat. Sb., 198:2 (2007), 121–160; Sb. Math., 198:2 (2007), 261–298

Citation in format AMSBIB
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  • https://doi.org/10.4213/sm1318
  • http://mi.mathnet.ru/eng/msb/v198/i2/p121

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    Citing articles on Google Scholar: Russian citations, English citations
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    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. I”, St. Petersburg Math. J., 20:1 (2009), 101–129  mathnet  crossref  mathscinet  zmath  isi
    2. B. N. Khabibullin, “Zero sequences of holomorphic functions, representation of meromorphic functions. II. Entire functions”, Sb. Math., 200:2 (2009), 283–312  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. 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”, Sb. Math., 200:9 (2009), 1353–1382  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. K. G. Malyutin, I. I. Kozlova, N. Sadik, “Canonical Functions of Admissible Measures in the Half-Plane”, Math. Notes, 96:3 (2014), 391–402  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    5. 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  mathnet  crossref  crossref  mathscinet  isi  elib
    6. B. N. Khabibullin, A. V. Shmelëva, “Vymetanie mer i subgarmonicheskikh funktsii na sistemu luchei. I. Klassicheskii sluchai”, Algebra i analiz, 31:1 (2019), 156–210  mathnet
  • Математический сборник Sbornik: Mathematics (from 1967)
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