Topics in Complex Analysis

Häftad, Engelska, 1996

699 kr

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This book is an outgrowth of lectures given at several occasions at the University of Goteborg and Chalmers University of Technology during the last ten years. Contrary to most introductory texts on complex analysis, it preassumes knowledge of basic analysis. This makes it possible to move rather quickly through the most fundamental material and to reach within a one-semester course some classical highlights such as Fatou theorems and some Nevanlinna theory, as well as more recent topics, for example the corona theorem and the H1-BMO duality.

Produktinformation

Utgivningsdatum1996-11-15
Mått155 x 235 x undefined mm
FormatHäftad
SpråkEngelska
SerieUniversitext
Antal sidor157
FörlagSpringer-Verlag New York Inc.
ISBN9780387947549

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Beräkning och matematisk analys inom Naturvetenskap och teknik

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.