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

2007/10/02 by Markiyan Hirnyk, Hirnyk, Markiyan
Mathematics · Medicine · #30E10 #31A05 #Analytic and geometric function theory #Complement (music) #Complex Variables (math.CV) #Constant (computer programming) #Endometriosis Research and Treatment #FOS: Mathematics #Function (biology) #Geometry #Logarithm #Mathematical analysis #Mathematics #Meromorphic and Entire Functions #Moduli #Nonlinear system #Order (exchange) #Physics #Point (geometry) #Pure mathematics #Set (abstract data type) #Subharmonic #Subharmonic function #math.CV #msc:30E10 #msc:31A05

paper · pdf · doi:10.48550/arxiv.0710.0592

12 pages, LATEX

arxiv created 2007/10/02 · openalex publication_date 2007/10/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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 Clog|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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