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Sbornik: Mathematics, 2009, Volume 200, Issue 2, Pages 283–312
DOI: https://doi.org/10.1070/SM2009v200n02ABEH003996 (Mi sm3885) 		 
This article is cited in 23 scientific papers (total in 23 papers)

Zero sequences of holomorphic functions, representation of meromorphic functions. II. Entire functions

B. N. Khabibullinab

a Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences
b Bashkir State University, Faculty of Mathematics
English version PDF (526 kB) Citations (23)
References:
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DOI: https://doi.org/10.1070/SM2009v200n02ABEH003996
Abstract: Let $\Lambda=\{\lambda_k\}$ be a sequence of points in the complex plane $\mathbb C$ and $f$ a non-trivial entire function of finite order $\rho$ and finite type $\sigma$ such that $f=0$ on $\Lambda$. Upper bounds for functions such as the Weierstrass-Hadamard canonical product of order $\rho$ constructed from the sequence $\Lambda$ are obtained. Similar bounds for meromorphic functions are also derived. These results are used to estimate the radius of completeness of a system of exponentials in $\mathbb C$.
Bibliography: 26 titles.
Keywords: function, zero sequence, subharmonic function, radius of completeness, system of exponentials.
Received: 22.05.2007 and 12.08.2008
Russian version:
Matematicheskii Sbornik, 2009, Volume 200, Number 2, Pages 129–158
DOI: https://doi.org/10.4213/sm3885
Bibliographic databases:
UDC: 517.547.2+517.538.2+517.581+517.574
MSC: 30C15, 30D15, 30D30
Language: English
Original paper language: Russian
Citation: B. N. Khabibullin, “Zero sequences of holomorphic functions, representation of meromorphic functions. II. Entire functions”, Mat. Sb., 200:2 (2009), 129–158; Sb. Math., 200:2 (2009), 283–312
Citation in format AMSBIB
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