单位圆盘上Pseudo-hyperbolic度量的应用  

The Application of Pseudo-hyperbolic Disk on Unit Disk

作　　者：杨克贲[1] 

机构地区：[1]西安工业大学数理系,西安710032

出　　处：《西安工业大学学报》2010年第1期100-102,共3页Journal of Xi’an Technological University

摘　　要：研究了单位圆盘上解析自映射在Pseudo-hyperbolic度量圆中的性质以及任意两个Schwarz-Pick导数的距离.运用了Pseudo-hyperbolic度量的一系列性质,得到了Pseudo-hy-perbolic度量圆中解析自映射在不同点下的相对变化规律,以及任意两个Schwarz-Pick导数的欧氏距离的Pseudo-hyperbolic度量的估计.这些性质对单位圆盘上复合算子的本性范数,差分紧性和空间拓扑结构的研究具有理论意义.This paper shows the properties of analytic self-maps of unit disk in Pseudo-hyperbolic metric disk and the distance of any two Schwarz-Pick type derivatives. The relative changes of analytic self-maps in different points in Pseudo-hyperbolic metric disk are gotten and the Euclidean distance of any two Schwarz-Pick type derivatives is estimated by using Pseudo-hyperbolic metric. These properties have theoretical significance in study of essential norm of composition operators, compactness of difference and topological structure on spaces.

关 键 词：对合自同构 解析自映射 Pseudo—hyperbolic度量 Schwarz—Pick导数 

分 类 号：O174.56[理学—数学]