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JOURNALS // Matematicheskii Sbornik // Archive

Mat. Sb., 2009 Volume 200, Number 2, Pages 129–158 (Mi sm3885)

This article is cited in 22 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

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.

UDC: 517.547.2+517.538.2+517.581+517.574

MSC: 30C15, 30D15, 30D30

Received: 22.05.2007 and 12.08.2008

DOI: 10.4213/sm3885


 English version:
Sbornik: Mathematics, 2009, 200:2, 283–312

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