Language: English
ISBN/ISSN: 7030084519
Published on: 2006-01
Hardcover
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book systematically summarizes the most important results in the field,including many of the authors'own previously unpublished results.In addition,useful skills and simple proofs are introduced.This book is suitable for higher level and graduate students who have a basic grounding in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.
Chapter 1 Basic Nivanlinna 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 th second fundamental theorem
1.6 Meromorphic functions with two Picard exceptional values
1.7 Combinations of meromorphic functions
2 Unicity 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 finits order
3 Five-value,multiple value and uniqueness
3.1 Nevanlinna's five-value theorem
3.2 Lo Yang's method
3.3 Nultiple values and uniqueness
3.4 Unicity of meromorphic functions of class A
3.5 Some general theorems on multiple value and unicity
4 The four-value theorem
4.1 Nevanlinna's four-value theorem
4.2 3CM+1IM values theorem
4.3 3CM+2IM values theorem
4.4 DM theorems for entire functions
4.5 4DM theorem
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 ofdifferential equations
5.5 The relationship between the characteristics
5.6 Mobius transformation
6 Three-value sets of meromorphic functions
6.1 Two-value sets of entire functions
6.2 three-value sets of meromorphic functions
7 Functions sharing one or two values
7.1 Functions sharing two common values
7.2 Functions sharing one common values
8 Functions shring values with their derives
8.1 Entire functions
8.2 Meromorphic functions
9 Two functions whose derivatives share values
9.1 Derivatives sharing common zeros
9.2 Derivatives sharing the value one
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 functions sharing one or two sets
10.5 Preimage and image sets of entire functions
10.6 Unique image sets of meromorphic functions
Bibliography
Index
