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.