A Modification of the Roper-Suffridge Extension Operator
A Modification of the Roper-Suffridge Extension Operator
复制标题
DOI：
10.1007/bf03321096
复制
发表时间：
2005-08
影响因子：
2.1
通讯作者：
Jerry R. Muir
中科院分区：
文献类型：
--
作者：
Jerry R. Muir
Roper-Suffridge扩张算子将定义在单位圆盘上的局部单叶映射扩张到定义在单位球上的局部双全纯映射。此外，一元凸映射或星形映射的扩张在多元情况下也具有类似的性质。受最近关于Kn中欧氏球的正规化凸映射族Kn的极值点的结果的启发，我们引入了一个新的扩张算子，在精确的条件下，它将K1的极值点带到Kn的极值点。在一般情况下，我们研究的条件下，这个新的扩展运营商将采取一个凸或星形映射的单位磁盘的映射相同类型的单位球上定义的。
The Roper-Suffridge extension operator extends a locally univalent mapping defined on the unit disk of ℂ to a locally biholomorphic mapping defined on the Euclidean unit ball of ℂn. Furthermore, the extension of a one variable mapping that is either convex or starlike has the analogous property in several variables. Motivated by recent results concerning the extreme points of the familyKnof normalized convex mappings of the Euclidean ball in ℂn, we introduce a new extension operator that, under precise conditions, takes the extreme points ofK1to extreme points ofKn. In general, we examine the conditions under which this new extension operator will take a convex or starlike mapping of the unit disk to a mapping of the same type defined on the unit ball.