亚纯函数值分布理论
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作者郑建华 著
出版社清华大学出版社
ISBN9787302223290
出版时间2010-06
版次1
装帧精装
开本16开
纸张胶版纸
页数308页
字数99999千字
定价68元
上书时间2024-07-01
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基本信息
书名:亚纯函数值分布理论
定价：68元
作者:郑建华 著
出版社：清华大学出版社
出版日期：2010-06-01
ISBN：9787302223290
字数：435000
页码：308
版次：1
装帧：精装
开本：16开
商品重量：
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内容提要
本书共7章，研究在复平面上或在以原点为顶点的角域上亚纯的函数的值分布，即通过某些值点来刻画亚纯函数。前两章研究各类特征函数及这样的实函数的性质。第3、4章放在新引入的奇异方向——T方向，包括存在性、分布，与其他方向的关系上，T方向与分布值和亏值总数的关系。射线分布值确定亚纯函数的增长性的问题在第5章详细研究。第6章研究亚纯函数对应的Riemann曲面，逆函数的奇异性及其与不动点的关系。最后一章介绍具有重要地位的ENevanlinna猜想的Eremenko应用位势论的证明。
目录
1 Preliminaries of Real Functions 1.1 Functions of a Real Variable 1.1.1 The Order and Lower Order of a Real Function 1.1.2 The P61ya Peak Sequence of a Real Function 1.1.3 The Regularity of a Real Function 1.1.4 Quasi-invariance of Inequalities 1.2 Integral Formula and Integral Inequalities 1.2.1 The Green Formula for Functions with Two Real Variables 1.2.2 Several Integral Inequalities References 2 Characteristics of a Meromorphic Function 2.1 Nevanlinna's Characteristic in a Domain 2.2 Nevanlinna's Characteristic in an Angle 2.3 Tsuji's Characteristic 2.4 Ahlfors-Shimizu's Characteristic 2.5 Estimates of the Error Terms 2.6 Characteristic of Derivative of a Meromorphic Function 2.7 Meromorphic Functions in an Angular Domain 2.8 Deficiency and Deficient Values 2.9 Uniqueness of Meromorphic Functions Related to Some Angular Domains References 3 T Directions of a Meromorphic Function 3.1 Notation and Estence of T Directions 3.2 T Directions Dealing with Small Functions 3.3 Connection Among T Directions and Other Directions 3.4 Singular Directions Dealing with Derivatives 3.5 The Common T Directions of a Meromorphic Function and Its Derivatives 3.6 Distribution of the Julia, Borel Directions and T Directions 3.7 Singular Directions of Meromorphic Solutions of Some Equations 3.8 Value Distribution of Algebroid Functions References 4 Argument Distribution and Deficient Values 4.1 Deficient Values and T Directions 4.2 Retrospection References 5 Meromorphic Functions with Radially Distributed Values 5.1 Growth of Such Meromorphic Functions 5.2 Growth of Such Meromorphic Functions with Finite Lower Order 5.3 Retrospection References 6 Singular Values of Meromorphic Functions 6.1 Riemann Surfaces and Singularities 6.2 Density of Singularities 6.3 Meromorphic Functions of Bounded Type References 7 The Potential Theory in Value Distribution 7.1 Signed Measure and Distributions 7.2 8-Subharmonic Functions 7.2.1 Basic Results Concerning 8-Subharmonic Functions 7.2.2 Normality of Family of 8-Subharmonic Functions 7.2.3 The Nevanlinna Theory of 8-Subharmonic Functions 7.3 Eremenko's Proof of the Nevanlinna Conjecture References Index
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