Value Distribution Of Meromorphic Functions Focuses On Functions Meromorphic In An Angle Or On The Complex Plane, T Directions, Deficient Values, Singular Values, Potential Theory In Value Distribution And The Proof Of The Celebrated Nevanlinna Conjecture. The Book Introduces Various Characteristics Of Meromorphic Functions And Their Connections, Several Aspects Of New Singular Directions, New Results On Estimates Of The Number Of Deficient Values, New Results On Singular Values And Behaviours Of Subharmonic Functions Which Are The Foundation For Further Discussion On The Proof Of The Nevanlinna Conjecture. The Independent Significance Of Normality Of Subharmonic Function Family Is Emphasized. This Book Is Designed For Scientists, Engineers And Post Graduated Students Engaged In Complex Analysis And Meromorphic Functions. Dr. Jianhua Zheng Is A Professor At The Department Of Mathematical Sciences, Tsinghua University, China. Preliminaries Of Real Functions -- Characteristics Of A Meromorphic Function -- T Directions Of A Meromorphic Function -- Argument Distribution And Deficient Values -- Meromorphic Functions With Radially Distributed Values -- Singular Values Of Meromorphic Functions -- The Potential Theory In Value Distribution. Jianhua Zheng. Includes Bibliographical References And Index.

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zlibzh/no-category/郑建华著, Jianhua Zheng, 郑建华著, 郑建华/亚纯函数值分布理论 英文版_35690332.pdf

Value Distribution of Meromorphic Functions

Zheng, Jianhua

Spektrum Akademischer Verlag. in Springer-Verlag GmbH

Springer ; Tsinghua University Press

Tsinghua University Press ; Springer

Steinkopff. in Springer-Verlag GmbH

Springer Berlin Heidelberg

Qinghua University Press

Scholars Portal

SpringerLink : Bücher, Berlin, Heidelberg, 2011

Beijing : Heidelberg ; New York, ©2011

Heidelberg, New York, Germany, 2010

China, People's Republic, China

Springer Nature, Beijing, 2011

Heidelberg, Beijing, ©2011

Di 1 ban, Beijing, 2010

Beijing, Berlin, 2010

Germany, Germany

1st, 2011

2019

Bookmarks: p1 (p1): 1 Preliminaries of Real Functions
p2 (p1): 1.1 Functions of a Real Variable
p3 (p1): 1.1.1 The Order and Lower Order of a Real Function
p4 (p4): 1.1.2 The Pólya Peak Sequence of a Real Function
p5 (p8): 1.1.3 The Regularity of a Real Function
p6 (p14): 1.1.4 Quasi-invariance of Inequalities
p7 (p19): 1.2 Integral Formula and Integral Inequalities
p8 (p19): 1.2.1 The Green Formula for Functions with Two Real Variables
p9 (p20): 1.2.2 Several Integral Inequalities
p10 (p23): References
p11 (p25): 2 Characteristics of a Meromorphic Function
p12 (p26): 2.1 Nevanlinna's Characteristic in a Domain
p13 (p47): 2.2 Nevanlinna's Characteristic in an Angle
p14 (p58): 2.3 Tsuji's Characteristic
p15 (p66): 2.4 Ahlfors-Shimizu's Characteristic
p16 (p77): 2.5 Estimates of the Error Terms
p17 (p86): 2.6 Characteristic of Derivative of a Meromorphic Function
p18 (p93): 2.7 Meromorphic Functions in an Angular Domain
p19 (p103): 2.8 Deficiency and Deficient Values
p20 (p110): 2.9 Uniqueness of Meromorphic Functions Related to Some Angular Domains
p21 (p120): References
p22 (p123): 3 T Directions of a Meromorphic Function
p23 (p124): 3.1 Notation and Existence of T Directions
p24 (p130): 3.2 T Directions Dealing with Small Functions
p25 (p134): 3.3 Connection Among T Directions and Other Directions
p26 (p146): 3.4 Singular Directions Dealing with Derivatives
p27 (p151): 3.5 The Common T Directions of a Meromorphic Function and Its Derivatives
p28 (p163): 3.6 Distribution of the Julia,Borel Directions and T Directions
p29 (p166): 3.7 Singular Directions of Meromorphic Solutions of Some Equations
p30 (p178): 3.8 Value Distribution of Algebroid Functions
p31 (p181): References
p32 (p185): 4 Argument Distribution and Deficient Values
p33 (p186): 4.1 Deficient Values and T Directions
p34 (p202): 4.2 Retrospection
p35 (p205): References
p36 (p207): 5 Meromorphic Functions with Radially Distributed Values
p37 (p208): 5.1 Growth of Such Meromorphic Functions
p38 (p215): 5.2 Growth of Such Meromorphic Functions with Finite Lower Order
p39 (p222): 5.3 Retrospection
p40 (p228): References
p41 (p229): 6 Singular Values of Meromorphic Functions
p42 (p230): 6.1 Riemann Surfaces and Singularities
p43 (p241): 6.2 Density of Singularities
p44 (p252): 6.3 Meromorphic Functions of Bounded Type
p45 (p265): References
p46 (p267): 7 The Potential Theory in Value Distribution
p47 (p268): 7.1 Signed Measure and Distributions
p48 (p270): 7.2 δ-Subharmonic Functions
p49 (p271): 7.2.1 Basic Results Concerning δ-Subharrnonic Functions
p50 (p275): 7.2.2 Normality of Family of δ-Subharmonic Functions
p51 (p285): 7.2.3 The Nevanlinna Theory of δ-Subharmonic Functions
p52 (p292): 7.3 Eremenko's Proof of the Nevanlinna Conjecture
p53 (p305): References
p54 (p307): Index

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Includes bibliographical references.

This book focuses on meromorphic functions in an angle or on the complex plane, T directions, deficient values, singular values, potential theory in value distribution and the proof of the Nevanlinna conjecture. It presents new aspects and covers new results.

本书共7章, 研究在复平面上或以原点为顶点的角域上亚纯的函数的值分布, 即通过某些值点来核画亚纯函数.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和第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F. Nevanlinna猜想的Eremenko应用位势论的证明

2024-06-13