亚纯函数值分布理论

所属分类:数学  
出版时间:2010-6   出版时间:清华大学出版社   作者:郑建华   页数:308  

前言

This book is devoted to the study of value distribution of functions which are mero-morphic on the complex plane or in an angular domain with vertex at the origin. Wecharacterize such meromorphic functions in terms of distribution of some of theirvalue points. The study, together with certain related topics, is known as theory ofvalue distribution of meromorphic functions. The theory is too vast to be justifiedwithin a single work. Therefore we selected and organized the content based on theirsignificant importance to our understanding and interests in this book. I gladly ac-knowledge my indebtedness in particular to the books of M. Tsuji, A. A. Goldbergand I. V. Ostrovskii, Yang L. and the papers of A. Eremenko.   An outline of the book is provided below. The introduction of the Nevanlinnacharacteristic to the study of meromorphic functions is a new starting symbol ofthe theory of value distribution. The Nevanlinna characteristic is powerful, and itsthought has been used to produce various characteristics such as the Nevanlinnacharacteristic and Tsuji characteristic for an angular domain. And from geometricpoint of view, namely the Ahlfors theory of covering surfaces, the Ahlfors-Shimizucharacteristic have also been introduced. These characteristics are real-valued func-tions defined on the positive real axis. Therefore, in the first chapter, we collect thebasic results about positive real functions that are often used in the study of mero-morphic function theory. Some of these results are distributed in other books, somein published papers, and some have been newly established in order to serve ourspecific objectives in the book.

内容概要

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。

作者简介

郑建华,Dr. Jianhua Zheng is a Professor at the Department of MathematicalSciences, Tsinghua University, China.

书籍目录

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

章节摘录

插图:

编辑推荐

《亚纯函数值分布理论》:Value Distribution of Meromorphic Functions focuses on functionsmeromorphic in an angle or on the complex plane, T directions, deficientvalues, singular values, potential theory in value distribution and theproof of the celebrated Nevanlinna conjecture. The book introducesvarious characteristics of meromorphic functions and their connections,several aspects of new singular directions, new results on estimates of thenumber of deficient values, new results on singular values and behavioursof subharmonic functions which are the foundation for further discussionon the proof of the Nevanlinna conjecture. The independent significanceof normality of subharmonic function family is emphasized. This book isdesigned for scientists, engineers and post graduated students engaged inComplex Analysis and Meromorphic Functions.

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用户评论 (总计2条)

 
 

  •     书很好, 很完整, 结果很新, 很喜欢
  •     好多年没有值分布的新书出版啦,很难得啊。
 

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