Uniqueness Theory of Meromorphic Functions

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Springer Science & Business Media, 04.10.2004 - 569 Seiten
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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book systematically summarizes the most important results in the field, including many of the authors' own previously unpublished results.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.
 

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Inhalt

Basic Nevanlinna theory
x
12 The second fundamental theorem
13
13 Some results on the characteristic function and the order
26
14 Value distribution of a meromorphic function and its linear combinations of derivatives
36
15 Generalizations of the second fundamental theorem
50
16 Meromorphic functions with two Picard exceptional values
61
17 Theorems related to combinations of meromorphic functions
70
Unicity of functions of finite lower order
96
52 Deficient values and unicity
281
53 Unicity of periodic or even functions
295
54 Unicity of solutions of differential equations
300
55 The relationship between the characteristics
308
56 Möbius transformation
318
Threevalue sets of meromorphic functions
338
62 Threevalue sets of meromorphic functions
350
Functions sharing one or two common values
364

22 Unicity of meromorphic functions of order 1
108
23 Functions of finite noninteger lower order
113
24 Unicity of entire functions with finite lower order
124
25 Taylor expansions of entire functions with finite order
146
Fivevalue multiple value and uniqueness
156
32 Lo Yangs method in dealing with the multiple values problems
171
33 Multiple values and uniqueness
179
34 Unicity of meromorphic functions of class A
192
35 Some general theorems on multiple value and unicity
202
The fourvalue theorem
215
42 3CM + 1IM values theorem
224
43 2CM + 2IM values theorem
231
44 DM theorems for entire functions
248
45 4DM theorem
253
Functions sharing three common values
273
72 Functions sharing one common value
371
Functions sharing values with their derivatives
384
82 Meromorphic functions sharing values with their derivatives
399
Two functions whose derivatives share values
426
92 Derivatives sharing the value one
436
Meromorphic functions sharing sets
454
102 Meromorphic functions sharing three sets
469
103 Meromorphic functions with deficient values
482
104 Meromorphic functions sharing one or two sets
492
105 Preimage and image sets of entire functions
500
106 Unique image sets of meromorphic functions
508
Bibliography
533
Index
566
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