On the Nevanlinna classes of holomorphic functions on compact bordered Riemann surfaces
type: Item
instance of: scholarly article
title: On the Nevanlinna classes of holomorphic functions on compact bordered Riemann surfaces
zbMATH Open document ID: 0708.30036
author: Yinian Lü
published in: Science in China. Series A
publication date: 1989-01-01T00:00:00Z
review text: This paper contains the generalization of the theorem of F. and R. Nevanlinna for the case of the holomorphic functions on the compact bordered Riemann surface \(\Omega\), which belong to the Nevanlinna class N(\(\Omega\)). (f\(\in N(\Omega)\) if the subharmonic function \(\log^+| f|\) has a harmonic majorant.) The author proved: A holomorphic function f belongs to N(\(\Omega\)) iff it is the quotient of two functions being holomorphic in \(\Omega\). This theorem is used to the study of the boundary behaviour of holomorphic functions from the class N(\(\Omega\)).
Mathematics Subject Classification ID: 30D50
Mathematics Subject Classification ID: 30F15
Mathematics Subject Classification ID: 30F99
zbMATH DE Number: 4163231
zbMATH Keywords: normal exhaustion
zbMATH Keywords: Green's function
zbMATH Keywords: compact bordered Riemann surface
zbMATH Keywords: Nevanlinna class
reviewed by: A. Klíč
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4163231