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

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

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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

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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• http://mi.mathnet.ru/eng/msb1318
• https://doi.org/10.4213/sm1318
• http://mi.mathnet.ru/eng/msb/v198/i2/p121

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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
2. B. N. Khabibullin, “Zero sequences of holomorphic functions, representation of meromorphic functions. II. Entire functions”, Sb. Math., 200:2 (2009), 283–312
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
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
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
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
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