Accuracy of approximation of subharmonic functions by logarithms of moduli of analytic ones in Chebyshev metrics

Details Accuracy of approximation of subharmonic functions by logarithms of moduli of analytic ones in Chebyshev metrics Accuracy of approximation of subharmonic functions by logarithms of moduli of analytic ones in Chebyshev metrics

2007-10-02

arxiv.org/abs/0710.0592v1

Mathematics

Complex Variables

12 pages, LATEX

Scientific paper

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.

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