內容提要
This book provides a concise treatment of topics in complex analysis, suitable for a one-semester course. It is an outgrowth of lectures given by the author over the last ten years at the University of Göteborg and chalmers university of technology. While treating classical complex function theory, the author emphas
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目錄
Preface
Preliminaries
1. Notation
2. Some Facts
1 Some Basic Properties of Analytic Functions
1. Conformal Mappings
2. Power Series Expansions and Residues
3. Global Cauchy Theorems
2 Properties of Analytic Mappings
1. Conformal Mappings
2. The Riemann Sphere and Projective Space
3.univalentFunctions
4. Picard's Theorems
3 Analytic Approximation and Continuation
1. Approximation with Rationals
2. Mittag-Leffler's Theorem and the Inhomogeneous Cauchy-Riemann Equation
3. Analytic Continuation
4. Simply Connected Domains
5. Analytic Functionals and the Fourier-Laplace
6. Mergelyan's Theorem
4 Harmonic and Subharmonic Functions
1. Harmonic Functions
2. Subharmonic Functions
5 Zeros, Growth, and Value Distribution
1. Weierstrass' Theorem
2. Zeros and Growth
3. Value Distribution of Entire Functions
6 Harmonic Functions and Fourier Series
1. Boundary Values of Harmonic Functions
2. Fourier Series
7 Hp Spaces
1. Factorization in Hp Spaces
2. Invariant Subspaces of H2
3. Interpolation of H8
4.CarlesonMeasures
8 Ideals and the Corona Theorem
1. Ideals in A
2. The Corona Theorem
9 H1 and BMO
1. Bounded Mean Oscillation
2. The Duality of H1 and BMO
Bibliography
List of Symbols
Index