亚纯函数值分布理论
图书信息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
出版时间： 2010-6-1
开本： 16开
I S B N ： 9787302223290
所属分类： 图书 >> 自然科学 >> 数学 >> 函数
定价：￥68.00
内容简介本书共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 Existence 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