《亞純函式唯一性理論》是2003年科學出版社出版的圖書，作者是Chung-Chun，YangHong-XunYi。
基本介紹
- 書名：亞純函式唯一性理論
- 作者：Chung-ChunYang，Hong-XunYi
- ISBN：9787030084514
- 頁數：569
- 定價：110.00元
- 出版社：科學出版社
- 出版時間：2003-12
- 裝幀：簡裝本
內容簡介,目錄,
內容簡介
《Uniqueness Theory of Meromorphic Functions》主要內容包括：This book is the first monograph in the field of uniqueness theory of meromorphic functions dealing with conditions under which there is the unique function satisfying given hypotheses.Developed by R.Nevanlinna，a Finnish mathematician，early in the 1920's，research in the field has developed rapidly over the past three decades with a great deal of fruitful results.This book systematically summarizes the most important results in the field，including many of the authors'own previously unpublished results.In addition，useful skills and simple proofs are introduced.This book is suitable for higher level and graduate students who have a basic grounding in complex analysis，but will also appeal to researchers in mathematics。
目錄
Preface
Chapter 1 Basic Nevanlinna theory
1.1 The first fundamental theorem
1.2 The second fundamental theorem
1.3 The characteristic function and the order
1.4 The combination of derivatives
1.5 Generalizations of the second fundamental theorem
1.6 Meromorphic functions with two Picard exceptional values
1.7 Combinations of meromorphic functions
Chapter 2 Uniclty of functions of finite (lower) order
2.1 Hadamard's factorization theorem
2.2 Unicity of meromorphic functions of order < 1
2.3 Functions of finite non-integer (lower) order
2.4 Unicity of entire functions with finite (lower) order
2.5 Taylor expansions of entire functions with finite order
Chapter 3 Five-value, multiple value and uniqueness
3.1 Nevanlinna's five-value theorem
3.2 Lo Yang's method
3.3 Multiple values and uniqueness
3.4 Unicity of meromorphic functions of class A
3.5 Some general theorems on multiple value and unicity
Chapter 4 The four-value theorem
4.1 Nevanlinna's four-value theorem
4.2 3CM + 1IM values theorem
4.3 2CM + 2IM values theorem
4.4 DM theorems for entire functions
4.5 4DM theorem
Chapter 5 Functions sharing three common values
5.1 Nevanlinna's three-value theorem
5.2 Deficient values and unicity
5.3 Unicity of periodic or even functions
5.4 Unicity of solutions of differential equations
5.5 The relationship between the characteristics
5.6 MSbius transformation
Chapter 6 Three-value sets of meromorphic functions
6.1 Two-value sets of entire functions
6.2 Three-value sets of meromorphic functions
Chapter 7 Functions sharing one or two values
7.1 Functions sharing two common values
7.2 Functions sharing one common value
Chapter 8 Functions sharing values with their derivatives
8.1 Entire functions
8.2 Meromorphic functions
Chapter 9 Two functions whose derivatives share values
9.1 Derivatives sharing common zeros
9.2 Derivatives sharing the value one
Chapter 10 Meromorphic functions sharing sets
10.1 Meromorphic functions sharing four sets
10.2 Meromorphic functions sharing three sets
10.3 Meromorphic functions with deficient values
10.4 Meromorphic fimctions sharing one or two sets
10.5 Preimage and image sets of entire functions
10.6 Unique image sets of meromorphic functions
Bibliography
Chapter 1 Basic Nevanlinna theory
1.1 The first fundamental theorem
1.2 The second fundamental theorem
1.3 The characteristic function and the order
1.4 The combination of derivatives
1.5 Generalizations of the second fundamental theorem
1.6 Meromorphic functions with two Picard exceptional values
1.7 Combinations of meromorphic functions
Chapter 2 Uniclty of functions of finite (lower) order
2.1 Hadamard's factorization theorem
2.2 Unicity of meromorphic functions of order < 1
2.3 Functions of finite non-integer (lower) order
2.4 Unicity of entire functions with finite (lower) order
2.5 Taylor expansions of entire functions with finite order
Chapter 3 Five-value, multiple value and uniqueness
3.1 Nevanlinna's five-value theorem
3.2 Lo Yang's method
3.3 Multiple values and uniqueness
3.4 Unicity of meromorphic functions of class A
3.5 Some general theorems on multiple value and unicity
Chapter 4 The four-value theorem
4.1 Nevanlinna's four-value theorem
4.2 3CM + 1IM values theorem
4.3 2CM + 2IM values theorem
4.4 DM theorems for entire functions
4.5 4DM theorem
Chapter 5 Functions sharing three common values
5.1 Nevanlinna's three-value theorem
5.2 Deficient values and unicity
5.3 Unicity of periodic or even functions
5.4 Unicity of solutions of differential equations
5.5 The relationship between the characteristics
5.6 MSbius transformation
Chapter 6 Three-value sets of meromorphic functions
6.1 Two-value sets of entire functions
6.2 Three-value sets of meromorphic functions
Chapter 7 Functions sharing one or two values
7.1 Functions sharing two common values
7.2 Functions sharing one common value
Chapter 8 Functions sharing values with their derivatives
8.1 Entire functions
8.2 Meromorphic functions
Chapter 9 Two functions whose derivatives share values
9.1 Derivatives sharing common zeros
9.2 Derivatives sharing the value one
Chapter 10 Meromorphic functions sharing sets
10.1 Meromorphic functions sharing four sets
10.2 Meromorphic functions sharing three sets
10.3 Meromorphic functions with deficient values
10.4 Meromorphic fimctions sharing one or two sets
10.5 Preimage and image sets of entire functions
10.6 Unique image sets of meromorphic functions
Bibliography
