On the boundary behavior of functions for which the Riemann image has finite spherical area
type: Item
instance of: scholarly article
title: On the boundary behavior of functions for which the Riemann image has finite spherical area
zbMATH Open document ID: 0591.30031
author: James A. Jenkins
author: Kôtaro Oikawa
published in: Kodai Mathematical Journal
publication date: 1985-01-01T00:00:00Z
review text: In this paper there is proved the following result and a number of applications of it are given. Let f be meromorphic in the half-strip \(S: a<x<b\), \(y>0\) and let the Riemann image of S by f have finite spherical area. Let \(\sigma\) denote the boundary point of S at the point at infinity. Let T be a closed subset of S such that for fixed \(L>0\) every rectangle \(a<x<b\), \(Y\leq y\leq Y+L\) (Y\(\geq 0)\) contains a subcontinuum of T of diameter \(\geq \delta\), \(\delta >0\). Let U be a subset of \(a'\leq x\leq b'\), \(y>0\) with \(a<a'<b'<b\). Then for the cluster sets of f at \(\sigma\) on T and U we have \(C(f,T,\sigma)\supset C(f,U,\sigma)\).
Mathematics Subject Classification ID: 30D40
zbMATH DE Number: 3948689
zbMATH Keywords: Riemann image
zbMATH Keywords: finite spherical area
zbMATH Keywords: boundary point
zbMATH Keywords: cluster sets
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138037099
OpenAlex ID: W2091351966
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DOI: 10.2996/KMJ/1138037099
description: scientific article; zbMATH DE number 3948689