The Cauchy Transform, Potential Theory and Conformal Mapping - Bell, Steven R
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The book provides a fast track to understanding the Riemann Mapping Theorem. The Dirichlet and Neumann problems for the Laplace operator are solved, the Poisson kernel is constructed, and the inhomogenous Cauchy-Reimann equations are solved concretely and efficiently using formulas stemming from the Kerzman-Stein result. Also, four new chapters have been added: two on quadrature domains and another two on complexity of the objects of complex analysis and improved Riemann mapping theorems.

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Produktbeschreibung
The book provides a fast track to understanding the Riemann Mapping Theorem. The Dirichlet and Neumann problems for the Laplace operator are solved, the Poisson kernel is constructed, and the inhomogenous Cauchy-Reimann equations are solved concretely and efficiently using formulas stemming from the Kerzman-Stein result. Also, four new chapters have been added: two on quadrature domains and another two on complexity of the objects of complex analysis and improved Riemann mapping theorems.
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Autorenporträt
Steven R. Bell, PhD, professor, Department of Mathematics, Purdue University, West Lafayette, Indiana, USA, and Fellow of the AMS