A Heuristic Principle in Complex Function Theory
A Heuristic Principle in Complex Function Theory
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DOI：
10.1080/00029890.1975.11993942
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发表时间：
1975-10
影响因子：
0.5
通讯作者：
L. Zalcman
中科院分区：
文献类型：
--
作者：
L. Zalcman
1.导论.函数论中一个著名的启发式原理断言”一个在域D中具有共同性质Pin的全纯（亚纯）函数族是（倾向于）D中的正规族，如果P不能被有限平面中的非常数整（亚纯）函数所拥有”[4，p. 250]。在他最近向符号逻辑协会（Association for Symbolic Logic）[7]发表的退休主席演讲中（任何对数学感兴趣的人都必须阅读阅读），已故教授亚伯拉罕·罗宾逊（Abraham Robinson）将这一原理的解释列为值得逻辑学家（以及一般数学家）关注的12个问题之一。准确地说，我们证明了一个简单的定理，使该原则严格，并从该原则的标准应用程序遵循相当常规。其中一些应用在最后指出，连同一个稍微新颖的方法来证明皮卡德的大定理。
1. Introduction. A well-known heuristic principle in the theory of functions asserts that" a family of holomorphic (meromorphic) functions which have a property Pin common in a domain D is (apt to be) a normal family in D if P cannot be possessed by non-constant entire (meromorphic) functions in the finite plane"[4, p. 250]. In his recent retiring presidential address to the Association for Symbolic Logic [7](required reading for anyone whose interests extend across professional boundaries to mathematics as an intellectual discipline), the late Professor Abraham Robinson cited the explication of this principle as one of twelve problems worthy of the attention of logicians (and, by extension, of mathematicians in general).This paper is devoted to such an explication. To be precise, we prove a simple theorem which makes the principle rigorous and from which the standard applications of the principle follow quite routinely. Some of these applications are noted at the end, together with a slightly novel approach to the proof of Picard's big theorem.