图书信息

内容简介

目录

图书信息

亚纯函数值分布理论作　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