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

Markiyan Hirnyk

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arXiv · 0710.0592

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

Markiyan Hirnyk

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Abstract

It is known that a subharmonic function of finite order $ρ$ 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 $C=ρ/4$, 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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BibTeX RIS

Markiyan Hirnyk. 2007-10-02. Accuracy of approximation of subharmonic functions by logarithms of moduli of analytic ones in Chebyshev metrics. https://arxiv.org/abs/0710.0592

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