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

This article is cited in 9 scientific papers (total in 9 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.


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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
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
\by B.~N.~Khabibullin
\paper Zero sequences of holomorphic functions, representation
of~meromorphic functions, and harmonic minorants
\jour Mat. Sb.
\yr 2007
\vol 198
\issue 2
\pages 121--160
\jour Sb. Math.
\yr 2007
\vol 198
\issue 2
\pages 261--298

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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. Shmelyova, “Balayage of measures and subharmonic functions on a system of rays. I. Classic case”, St. Petersburg Math. J., 31:1 (2020), 117–156  mathnet  crossref  isi  elib
    7. 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
    8. 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
    9. E. B. Menshikova, B. N. Khabibullin, “Kriterii posledovatelnosti kornei golomorfnoi funktsii s ogranicheniyami na ee rost”, Izv. vuzov. Matem., 2020, no. 5, 55–61  mathnet  crossref
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