Extension operators for locally univalent mappings
type: Item
instance of: scholarly article
title: Extension operators for locally univalent mappings
zbMATH Open document ID: 1025.32017
author: I. Graham
author: H. Hamada
author: G. Kohr
author: Ted J. Suffridge
published in: Michigan Mathematical Journal
publication date: 2003-06-30T00:00:00Z
review text: In the paper the following operators are studied \[ \Psi_{n, \alpha,\beta} (f)(z)=\left( f(z_1),\left( {f(z_1)\over z_1}\right)^\alpha \bigl( f(z_1)\bigr)^\beta z'\right),\;z\in B^n, \] where \(B^n=\{z\in \mathbb{C}^n:\|z \|<1\}\), \(z=(z_1,z')\), \(\alpha\geq 0\), \(\beta\geq 0\) and \(f\) is a locally univalent function on the unit disk, normalized by \(f(0)=f'(0)-1=0\), and such that \(f(z_1)\neq 0\), for \(z_1\neq 0\). Using these operators, the authors have generated linear-invariant families and investigate them.
Mathematics Subject Classification ID: 32H02
Mathematics Subject Classification ID: 32A17
Mathematics Subject Classification ID: 32A30
zbMATH DE Number: 1943208
zbMATH Keywords: holomorphic mapping
zbMATH Keywords: Loewner chain
zbMATH Keywords: linear-invariant family
reviewed by: P. Z. Agranovich
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1022636749
OpenAlex ID: W2080002196
DOI: 10.1307/MMJ/1022636749
description: scientific article; zbMATH DE number 1943208