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It is known that a subharmonic function of finite order $\rho$ can be approximated by the logarithm of the modulus of an entire function at the point $z$ outside an exceptional set up to $C\log|z|$. In this article we prove that if such an approximation is made more precise, i. e. a constant $C$ decreases, then, beginning with $C=\rho/4$, the size of the exceptional set enlarges substantially. Similar results are proved for subharmonic functions of infinite order and functions subharmonic in the unit disk. These theorems improve and complement a result by Yulmukhametov.

Author

Hirnyk, Markiyan

Published

2007

Language

EN