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The Cauchy Transform, Potential Theory and Conformal Mapping, 2nd Edition.

By: Bell, Steven R.
Material type: TextTextSeries: eBooks on Demand.Publisher: Boca Raton : CRC Press, 2015Edition: 2nd ed.Description: 1 online resource (221 p.).ISBN: 9781498727211.Genre/Form: Electronic books.Additional physical formats: Print version:: The Cauchy Transform, Potential Theory and Conformal Mapping, 2nd EditionDDC classification: 515.9 LOC classification: QA360Online resources: Click here to view this ebook.
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 -- Back Cover
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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 -- Back Cover

Description based upon print version of record.

Author notes provided by Syndetics

<p>Steven R. Bell, PhD, professor, Department of Mathematics, Purdue University, West Lafayette, Indiana, USA, and Fellow of the AMS</p>

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