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The Cauchy transform, potential theory, and conformal mapping

Author: Steven Robert Bell
Publisher: Boca Raton : CRC Press, Taylor & Francis Group, [2016]
Edition/Format:   Print book : English : 2nd editionView all editions and formats
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Additional Physical Format: Erscheint auch als:
Bell, Steven Robert,
The Cauchy transform, potential theory, and conformal mapping
Boca Raton : CRC Press, 2016
1 online resource (xii, 206 pages)
Online-Ausgabe
Document Type: Book
All Authors / Contributors: Steven Robert Bell
ISBN: 9781498727204 1498727204
OCLC Number: 913768203
Notes: "A Chapman & Hall book."
Description: xii, 209 pages ; 24 cm
Contents: Introduction --
The improved Cauchy integral formula --
The Cauchy transform --
The Hardy space, Szegő projection, and Kerzman-Stein formula --
The Kerzman-Stein operator and kernel --
The classical definition of the Hardy space --
The Szegő kernel function --
The Riemann mapping function --
A density lemma and consequences --
Solution of the Dirichlet problem in simply connected domains --
The case of real analytic boundary --
The transformation law for the Szegő kernel --
The Ahlfors map of a multiply connected domain --
The Dirichlet problem in multiply connected domains --
The Bergman space --
Proper holomorphic mappings and the Bergman projection --
The Solid Cauchy transform --
The classical Neumann problem --
Harmonic measure and the Szegő kernel --
The Neumann problem in multiply connected domains --
The Dirichlet problem again --
Area quadrature domains --
Arc length quadrature domains --
The Hilbert transform --
The Bergman kernel and the Szegő kernel --
Pseudo-local property of the Cauchy transform --
Zeroes of the Szegő kernel --
The Kerzman-Stein integral equation --
Local boundary behavioir of holomorphic mappings --
The dual space of A --
The Green's function and the Bergman kernel --
Zeroes of the Bergman kernel --
Complexity in complex analysis --
Area quadrature domains and the double --
The Cauchy-Kovalevski theorem for the Cauchy-Riemann operator.
Responsibility: Steven R. Bell, Purdue University, West Lafayette, Indiana, USA.

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