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

B. N. Khabibullin

Sbornik. Mathematics, Tome 200 (2009) no. 2, pp. 283-312

Résumé

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.

Détail

Keywords: function, zero sequence, subharmonic function, radius of completeness, system of exponentials.

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