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Geometric Function Theory: Exploration in Complex Analysis

Steven G. Krantz
Publisher: 
Birkhäuser
Publication Date: 
2006
Number of Pages: 
314
Format: 
Hardcover
Series: 
Cornerstones
Price: 
69.95
ISBN: 
0-8176-4339-7
Category: 
Textbook
We do not plan to review this book.

* Preface

Part I: Classical Function Theory

* Invariant Geometry

* Variations on the Theme of the Schwarz Lemma

* Normal Families

* The Riemann Mapping Theorem and its Generalizations

* Boundary Regularity of Conformal Maps

* The Boundary Behavior of Holomorphic Functions

Part II: Real and Harmonic Analysis

* The Cauchy–Riemann Equations

* The Green's Function and the Poisson Kernel

* Harmonic Measure

* Conjugate Functions and the Hilbert Transform

* Wolff's Proof of the Corona Theorem

Part III: Algebraic Topics

* Automorphism Groups of Domains in the Plane

* Cousin Problems, Cohomology, and Sheaves

* Bibliography

* Index

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