Accuracy of approximation of subharmonic functions by logarithms of moduli of analytic ones in Chebyshev metrics
| dc.creator | Hirnyk, Markiyan | |
| dc.date | 2007-10-02 | |
| dc.date.accessioned | 2026-07-07T08:33:35Z | |
| dc.date.available | 2026-07-07T08:33:35Z | |
| dc.description | 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. | |
| dc.description | 12 pages, LATEX | |
| dc.identifier | https://arxiv.org/abs/0710.0592 | |
| dc.identifier | http://arxiv.org/abs/0710.0592 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/139182 | |
| dc.subject | Complex Variables | |
| dc.subject | 31A05, 30E10 | |
| dc.title | Accuracy of approximation of subharmonic functions by logarithms of moduli of analytic ones in Chebyshev metrics | |
| dc.type | text |