Nine Introductions in Complex Analysis
Published on 14. May 2014
732 pages
978-0-08-087164-6 (ISBN)
Description
Nine Introductions in Complex Analysis
More details
Series
Language
English
Place of publication
Amsterdam
Netherlands
Product notice
Windows
ISBN-13
978-0-08-087164-6 (9780080871646)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Sanford L. Segal
Nine Introductions in Complex Analysis: Volume 53
Book
04/2000
North-Holland
€185.70
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Content
- Front Cover
- Nine Introductions in Complex Analysis
- Copyright Page
- Table of Contents
- Foreword
- Chapter I. Conformal Mapping & Riemann Mapping Theorem
- I.1 Introduction
- I.2 Linear Fractional Transformations
- I.3 Univalent Functions
- I.4 Normal Families
- I.5 The Riemann Mapping Theorem
- Chapter II. Picard's Theorems
- II.1 The Bloch-Landau Approach
- II.2 The Elliptic Modular Function
- II.3 The Constants of Bloch and Landau
- Chapter III. An Introduction to Entire Functions
- III.1 Growth, Order, and Zeros
- III.2 Growth, Coefficients and Type
- III.3 The Phragmen-Lindelof Indicator
- III.4 Composition of Entire Functions
- Chapter IV. Introduction to Meromorphic Functions
- IV.1 Nevanlinna's Characteristics and its Elementary Properties
- IV.2 Nevanlinna's Second Fundamental Theorem
- IV.3 Nevanlinna's Second Fundamental Theorem: Some Applications
- Chapter V. Asymptotic Values
- V.1 Julia's Theorem
- V.2 The Denjoy-Carleman-Ahlfors Theorem
- Chapter VI. Natural Boundaries
- VI.1 Natural Boundaries--Some Examples
- VI.2 The Hadamard Gap Theorem and Over-convergence
- VI.3 The Hadamard Multiplication Theorem
- VI.4 The Fabry Gap Theorem
- VI.5 The Polya-Carlson Theorem
- Chapter VII. The Bieberbach Conjecture
- VII.1 Elementary Area and Distortion Theorems
- VII.2 Some Coefficient Theorems
- Chapter VIII. Elliptic Functions
- VIII.1 Elementary Properties
- VIII.2 Weierstrass' P-function
- VIII.3 Weierstrass' t-and a-functions
- VIII.4 Jacobi's Elliptic Functions
- VIII.5 Theta Functions
- VIII.6 Modular Functions
- Chapter IX. Introduction to the Riemann Zeta-Function
- IX.1 Prime Numbers and t(s)
- IX.2 Ordinary Dirichlet Series
- IX.3 The Functional Equation, the Prime Number Theorem, and De la Vallee-Poussin's Estimate
- IX.4 The Riemann Hypothesis
- Appendix
- I The Area Theorem
- II The Borel-Caratheodory Lemma
- III The Schwarz Reflection Principle
- IV A Special Case of the Osgood-Caratheodory Theorem
- V Farey Series
- VI The Hadamard Three Circles Theorem
- VII The Poisson Integral Theorem
- VIII Bernoulli Numbers
- IX The Poisson Summation Formula
- X The Fourier Integral Theorem
- Word List
- Bibliographic Remarks
