多圆盘的Busemann函数与Julia-Wolff-Caratheodory定理
Busemann Functions and Julia-Wolff-Caratheodory Theorem for Polydiscs
摘要：
经典的Julia-Wolff-Caratheodory定理是研究$\C$的单位圆盘上全纯自映射的边界表现的主要工具之一。本文证明了多圆盘$\C^n.$的Julia-Wolff-Caratheodory型定理。利用Busemann函数定义了多圆盘的一类“广义球面”，推广了非切向极限的概念。有了这些新的工具，我们给出了一个推广的经典朱莉娅引理和Lindelof定理，新的朱莉娅-沃尔夫-Caratheodory定理依赖。
英文摘要：
The classical Julia-Wolff-Caratheodory Theorem is one of the main tools to study the boundary behavior of holomorphic self-maps of the unit disc of $\C$. In this paper we prove a Julia-Wolff-Caratheodory's type theorem in the case of the polydisc of $\C^n.$ The Busemann functions are used to define a class of "generalized horospheres" for the polydisc and to extend the notion of non-tangential limit. With these new tools we give a generalization of the classical Julia's Lemma and of the Lindelof Theorem, which the new Julia-Wolff-Caratheodory Theorem relies upon.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
