Uniqueness Theory of Meromorphic FunctionsSpringer Science & Business Media, 2003 - 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book systematically summarizes the most important results in the field, including many of the authors' own previously unpublished results.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. |
Inhalt
Basic Nevanlinna theory | |
12 The second fundamental theorem | 11 |
13 Some results on the characteristic function and the order | 24 |
14 Value distribution of a meromorphic function and its linear combinations of derivatives | 34 |
15 Generalizations of the second fundamental theorem | 48 |
16 Meromorphic functions with two Picard exceptional values | 59 |
17 Theorems related to combinations of meromorphic functions | 68 |
Unicity of functions of finite lower order | 94 |
52 Deficient values and unicity | 279 |
53 Unicity of periodic or even functions | 293 |
54 Unicity of solutions of differential equations | 298 |
55 The relationship between the characteristics | 306 |
56 Möbius transformation | 316 |
Threevalue sets of meromorphic functions | 336 |
62 Threevalue sets of meromorphic functions | 348 |
Functions sharing one or two common values | 362 |
22 Unicity of meromorphic functions of order 1 | 106 |
23 Functions of finite noninteger lower order | 111 |
24 Unicity of entire functions with finite lower order | 122 |
25 Taylor expansions of entire functions with finite order | 144 |
Fivevalue multiple value and uniqueness | 154 |
32 Lo Yangs method in dealing with the multiple values problems | 169 |
33 Multiple values and uniqueness | 177 |
34 Unicity of meromorphic functions of class A | 190 |
35 Some general theorems on multiple value and unicity | 200 |
The fourvalue theorem | 213 |
42 3CM + 1IM values theorem | 222 |
43 2CM + 2IM values theorem | 229 |
44 DM theorems for entire functions | 246 |
45 4DM theorem | 251 |
Functions sharing three common values | 271 |
72 Functions sharing one common value | 369 |
Functions sharing values with their derivatives | 382 |
82 Meromorphic functions sharing values with their derivatives | 397 |
Two functions whose derivatives share values | 424 |
92 Derivatives sharing the value one | 434 |
Meromorphic functions sharing sets | 452 |
102 Meromorphic functions sharing three sets | 467 |
103 Meromorphic functions with deficient values | 480 |
104 Meromorphic functions sharing one or two sets | 490 |
105 Preimage and image sets of entire functions | 498 |
106 Unique image sets of meromorphic functions | 506 |
Bibliography | 531 |
Index | 564 |
Andere Ausgaben - Alle anzeigen
Uniqueness Theory of Meromorphic Functions Chung-Chun Yang,Hong-Xun Yi Keine Leseprobe verfügbar - 2010 |
Häufige Begriffe und Wortgruppen
1-points a₁ algebroid functions b₁ c₁ completes the proof complex plane coprime Corollary Let counting function ea(z Ef(S Eg(S equation eẞ(z f and g f-aj f₁ finite order following result following Theorem function f functions of finite functions that share g be non-constant g share implies Jensen formula Lemma Let f Let f(z linearly independent log+ lower order meromorphic functions satisfying meromorphic functions sharing Möbius transformation No(r non-constant entire function non-constant meromorphic functions non-zero constants order of f(z Picard exceptional values poles of f polynomial positive integer proof of Theorem prove Theorem proved the following rational functions S₁ second fundamental theorem Shandong share the value share three shared values sharing 0,1 Similarly small functions Suppose that f(z Theorem 4.4 transcendental meromorphic function Unicity theorems uniqueness of meromorphic values of f values of f(z zeros of f аз
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Verweise auf dieses Buch
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