THE MAIN RESULTS ON SUFFICIENT CONDITIONS FOR AN ANALYTIC FUNCTION TO BE SCHLICHT
THE MAIN RESULTS ON SUFFICIENT CONDITIONS FOR AN ANALYTIC FUNCTION TO BE SCHLICHT
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解析函数为SCHLICHT的充分条件的主要结果
DOI：
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发表时间：
1975
期刊：
影响因子：
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通讯作者：
L. A. Aksent’ev
中科院分区：
文献类型：
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作者：
F. Avkhadiev;L. A. Aksent’ev
本文阐述了从函数几何理论开始这一研究方向（三十年代）至今所获得的关于解析函数的不充分性的充分条件的结果。最后给出了简短的历史回顾。在第一章和第二章中，我们描述了经受住了时间考验的拙劣条件，这些条件以其推导的简单性和应用的丰富性而著称。在第三章中，我们对这个主题的更激烈的观点进行了描述：在我们看来，其中所规定的为恶行创造充分条件的原则是影响最深远的。在第四章中，我们以示意图的形式阐述了第一章至第三章结果的应用，并提到了一些问题。第五章涉及影响我们主题的问题，但不属于本文作者的主要兴趣。
This article gives an account of the results on sufficient conditions for schlichtness of analytic functions that have been obtained from the time (in the thirties) when this line of investigation started in the geometric theory of functions, up to the present. A brief historical survey is given at the end. In the first and second chapters we describe conditions for schlichtness that have stood the test of time and are distinguished by the simplicity of their derivations and the richness of their applications. In the third chapter we give a characterization of the more fiery points of the subject: the principles laid down there of constructing sufficient conditions for schlichtness are in our view the most far-reaching. In the fourth chapter we set out in schematic form applications of the results of Chapters I-III, and we mention a few problems. The fifth chapter is concerned with questions that impinge on our theme, but lie outside the main interests of the authors of this article.