A generalized Schwarz lemma at the boundary

被引：51

作者：

Chelst, D ^{[1
]}

机构：

[1] Rutgers State Univ, Dept Math, Piscataway, NJ 08854 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2001年 / 129卷 / 11期

关键词：

Schwarz's lemma; Schur functions; bounded analytic functions; Blaschke product;

D O I：

10.1090/S0002-9939-01-06144-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let phi be an analytic function mapping the unit disc D to itself. We generalize a boundary version of Schwarz's lemma proven by D. Burns and S. Krantz and provide sufficient conditions on the local behavior of phi near a finite set of boundary points that requires phi to be a finite Blaschke product. Afterwards, we supply several counterexamples to illustrate that these conditions may also be necessary.

引用

页码：3275 / 3278

页数：4