Uniqueness Theory of Meromorphic Functions

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book systematically summarizes the most important results in the field, including many of the authors' own previously unpublished results.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