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