Theory of entire and meromorphic functions : deficient and asymptotic values and singular directions / Guan-hou, Zhang

Por: Zhang, Guan-hou, 1937-1987Idioma: Inglés Lenguaje original: Chino Series Translations of mathematical monographs ; v. 122Editor: Providence, R.I. : American Mathematical Society, c1993Descripción: xi, 375 p. ; 26 cmISBN: 0821845896 (alk. paper)Títulos uniformes: Cheng han shu ho yeh chʻun han shu li lun. English Tema(s): Functions, Entire | Functions, MeromorphicOtra clasificación: *CODIGO*
Contenidos incompletos:
Contents --
Preface ix --
Chapter I. The Nevanlinna Theory [1] --
1.1. The Poisson-Jensen formula [1] --
1.2. The characteristic function [5] --
1.3. The Alhfors-Shimizu characteristic --
1.4. The First Fundamental Theorem [10] --
1.5. Lemma on the logarithmic derivative [14] --
1.6. The Second Fundamental Theorem [21] --
1.7. Annotated notes [33] --
Chapter 2. The Singular Directions [37] --
2.1. On some properties of monotonic functions [37] --
2.2. The Boutroux-Cartan Theorem [49] --
2.3. Fundamental theorem of value distribution of functions meromorphic in a disk [54] --
2.4. The Julia and Borel directions [73] --
2.5. On the growth of the entire function [88] --
2.6. On the Nevanlinna direction [100] --
2.7. Annotated notes [107] --
Chapter 3. The Deficient Value Theory [109] --
3.1. The harmonic measure and the Lindelof-type theorem [109] --
3.2. The Length-Area Principle [118] --
3.3. On the growth of meromorphic functions with deficient values 123 3.4. The Weitsman Theorem [144] --
3.5. The Edrei-Fuchs Theorem [158] --
3.6. Annotated notes [188] --
Chapter 4. The Asymptotic Value Theory [195] --
4.1. The asymptotic value and the transcendental singularity 195 4.2. The Denjoy Conjecture [208] --
4.3. Growth of entire functions along an asymptotic path [232] --
4.4. An estimate on the length of the asymptotic path of an enitre --
function [247] --
4.5. Direct transcendental singularities [257] --
Chapter 5. The Relationship between Deficient Values and Asymptotic Values of an Entire Function [271] --
5.1. The theorem of the bound and its application regarding functions meromorphic in the unit disk [271] --
5.2. Entire functions of finite lower order [282] --
5.3. On entire functions having a finite number of Julia directions [304] --
5.4. Extremal length and Ahlfors Distortion Theorem [319] --
5.5. On entire functions with zeros distributed on a finite number of half lines [330] --
Chapter 6. The Relationship between Deficient Values of a Meromorphic Function and Direct Transcendental Singularities of its Inverse Functions [349] --
6.1. On meromorphic functions having deficiency sum two [349] --
6.2. On meromorphic functions of finite lower order [358] --
Some Supplementary Results [369] --
--
References [371] --
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Includes bibliographical references (p. 371-375).

Contents --
Preface ix --
Chapter I. The Nevanlinna Theory [1] --
1.1. The Poisson-Jensen formula [1] --
1.2. The characteristic function [5] --
1.3. The Alhfors-Shimizu characteristic --
1.4. The First Fundamental Theorem [10] --
1.5. Lemma on the logarithmic derivative [14] --
1.6. The Second Fundamental Theorem [21] --
1.7. Annotated notes [33] --
Chapter 2. The Singular Directions [37] --
2.1. On some properties of monotonic functions [37] --
2.2. The Boutroux-Cartan Theorem [49] --
2.3. Fundamental theorem of value distribution of functions meromorphic in a disk [54] --
2.4. The Julia and Borel directions [73] --
2.5. On the growth of the entire function [88] --
2.6. On the Nevanlinna direction [100] --
2.7. Annotated notes [107] --
Chapter 3. The Deficient Value Theory [109] --
3.1. The harmonic measure and the Lindelof-type theorem [109] --
3.2. The Length-Area Principle [118] --
3.3. On the growth of meromorphic functions with deficient values 123 3.4. The Weitsman Theorem [144] --
3.5. The Edrei-Fuchs Theorem [158] --
3.6. Annotated notes [188] --
Chapter 4. The Asymptotic Value Theory [195] --
4.1. The asymptotic value and the transcendental singularity 195 4.2. The Denjoy Conjecture [208] --
4.3. Growth of entire functions along an asymptotic path [232] --
4.4. An estimate on the length of the asymptotic path of an enitre --
function [247] --
4.5. Direct transcendental singularities [257] --
Chapter 5. The Relationship between Deficient Values and Asymptotic Values of an Entire Function [271] --
5.1. The theorem of the bound and its application regarding functions meromorphic in the unit disk [271] --
5.2. Entire functions of finite lower order [282] --
5.3. On entire functions having a finite number of Julia directions [304] --
5.4. Extremal length and Ahlfors Distortion Theorem [319] --
5.5. On entire functions with zeros distributed on a finite number of half lines [330] --
Chapter 6. The Relationship between Deficient Values of a Meromorphic Function and Direct Transcendental Singularities of its Inverse Functions [349] --
6.1. On meromorphic functions having deficiency sum two [349] --
6.2. On meromorphic functions of finite lower order [358] --
Some Supplementary Results [369] --
--
References [371] --

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