A generalized Schwarz lemma at the boundary
type: Item
instance of: scholarly article
title: A generalized Schwarz lemma at the boundary
zbMATH Open document ID: 0981.30020
DOI: 10.1090/S0002-9939-01-06144-5
author: Dov Chelst
published in: Proceedings of the American Mathematical Society
publication date: 2001-07-30T00:00:00Z
Mathematics Subject Classification ID: 30C80
zbMATH DE Number: 1626794
zbMATH Keywords: Schwarz's lemma
zbMATH Keywords: Schur functions
zbMATH Keywords: Blaschke product
MaRDI profile type: Publication
cites work: Rigidity of Holomorphic Mappings and a New Schwarz Lemma at the Boundary
cites work: Q5187597
Wikidata QID: Q125011931
review text: \textit{D. Burns} and \textit{S. Krantz} [J. Am. Math. Soc. 7, No. 3, 661-676 (1994; Zbl 0807.32008)] proved, in particular, the following beautiful boundary version of Schwarz's lemma. Let \(\varphi\) be an analytic function mapping the unit disk \(\mathbb{D}\) into itself such that \(\varphi(z)=z+O((z-1)^4)\) as \(z\to 1\). Then \(\varphi(z)=z\) on the unit disk \(\mathbb{D}\). In the paper under review, the author's nice generalization of the above lemma extends to finite Blaschke products.
reviewed by: George Csordas
description: scientific article; zbMATH DE number 1626794