Extension operators and subordination chains
Extension operators and subordination chains
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DOI：
10.1016/j.jmaa.2011.07.064
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发表时间：
2012-02
影响因子：
1.3
通讯作者：
Ian D. Graham;H. Hamada;G. Kohr
中科院分区：
文献类型：
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作者：
Ian D. Graham;H. Hamada;G. Kohr
自从1995年Roper和Suffbridge的工作以来，人们一直对利用具有相似性质的低维映射来构造具有各种几何性质的单位球的全纯映射感兴趣。这些性质包括凸性、星形性和螺形性。扩展从属关系链(可能与上述几何属性相关)也是有意义的。最近，M.Elin引入了一种基于半群的Banach空间上扩张算子的方法，从而证明了这类算子的一些基本性质。本文采用ElinʼS的观点，证明了从属链扩张的一个定理，推广和统一了已有的结果。我们还考虑了在有限维上研究Loewner变差下的极值点和支撑点以及控制理论中的可达集的应用。还将提供一些例子。
Since the work of Roper and Suffridge in 1995, there has been considerable interest in constructing holomorphic mappings of the unit ball in Cnwith various geometric properties by using lower dimensional mappings with similar properties. Such properties include convexity, starlikeness, and spirallikeness. It is also of interest to extend subordination chains (which may be related to geometric properties such as the above). Recently M. Elin has introduced an approach to extension operators on Banach spaces based on semigroups which leads to an identification of some of the essential properties of such operators. In this paper we adopt Elinʼs point of view and prove a theorem about the extension of subordination chains which extends and unifies existing results. We also consider applications in finite dimensions to the study of extreme and support points under the Loewner variation and of reachable sets in control theory. Certain examples will also be provided.