Topics in Complex Analysis
This book is an outgrowth of lectures given on several occasions at Chalmers University of Technology and Goteborg University during the last ten years. As opposed to most introductory books on complex analysis, this one as sumes that the reader has previous knowledge of basic real analysis. This m...
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| Format: | eBook |
| Language: | English |
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New York, NY
Springer New York
1997, 1997
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| Edition: | 1st ed. 1997 |
| Series: | Universitext: Tracts in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- Preliminaries
- §1. Notation
- §2. Some Facts
- 1. Some Basic Properties of Analytic Functions
- §1. Definition and Integral Representation
- §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. Univalent Functions
- §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 Transform
- §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. IF Spaces
- §1. Factorization in Hp Spaces
- §2. Invariant Subspaces of H2
- §3. Interpolation of H?
- §4. Carleson Measures
- 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
- List of Symbols