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TitleThe Cauchy transform, potential theory, and conformal mapping
Author
LanguageEnglish
File Size3.8 MB
Total Pages221
Table of Contents
                            Front Cover
Contents
Preface
Table of symbols
Chapter 1 - Introduction
Chapter 2 - The improved Cauchy integral formula
Chapter 3 - The Cauchy transform
Chapter 4 - The Hardy space, the Szegő projection, and the Kerzman-Stein formula
Chapter 5 - The Kerzman-Stein operator and kernel
Chapter 6 - The classical definition of the Hardy space
Chapter 7 - The Szegő kernel function
Chapter 8 - The Riemann mapping function
Chapter 9 - A density lemma and consequences
Chapter 10 - Solution of the Dirichlet problem in simply connected domains
Chapter 11 - The case of real analytic boundary
Chapter 12 - The transformation law for the Szegő kernel under conformal mappings
Chapter 13 - The Ahlfors map of a multiply connected domain
Chapter 14 - The Dirichlet problem in multiply connected domains
Chapter 15 - The Bergman space
Chapter 16 - Proper holomorphic mappings and the Bergman projection
Chapter 17 - The Solid Cauchy transform
Chapter 18 - The classical Neumann problem
Chapter 19 - Harmonic measure and the Szegő kernel
Chapter 20 - The Neumann problem in multiply connected domains
Chapter 21 - The Dirichlet problem again
Chapter 22 - Area quadrature domains
Chapter 23 - Arc length quadrature domains
Chapter 24 - The Hilbert transform
Chapter 25 - The Bergman kernel and the Szegő kernel
Chapter 26 - Pseudo-local property of the Cauchy transform and consequences
Chapter 27 - Zeroes of the Szegő kernel
Chapter 28 - The Kerzman-Stein integral equation
Chapter 29 - Local boundary behavior of holomorphic mappings
Chapter 30 - The dual space of A∞(Ω)
Chapter 31 - The Green’s function and the Bergman kernel
Chapter 32 - Zeroes of the Bergman kernel
Chapter 33 - Complexity in complex analysis
Chapter 34 - Area quadrature domains and the double
Appendix A - The Cauchy-Kovalevski theorem for the Cauchy-Riemann operator
Bibliographic Notes
Bibliography
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