The Schwarz function originates in classical complex analysis and potential theory. Here the author presents the advantages favoring a mode of treatment which unites the subject with modern theory of distributions and partial differential equations thus bridging the gap between two-dimensional geometric and multi-dimensional analysts. Examines the Schwarz function and its relationship to recent investigations regarding inverse problems of Newtonian gravitation, free boundaries, Hele-Shaw flows and the propagation of singularities for holomorphic p.d.e.
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The Schwarz Principle of Reflection.
The Logarithmic Potential, Balayage, and Quadrature Domains.
Examples of ``Quadrature Identities''.
Quadrature Domains: Basic Properties, 1.
Quadrature Domains: Basic Properties, 2.
Schwarzian Reflection, Revisited.
Projectors from L? (dOmega) to H? (dOmega).
The Friedrichs Operator.
Concluding Remarks.
Bibliography.
Index.
The Logarithmic Potential, Balayage, and Quadrature Domains.
Examples of ``Quadrature Identities''.
Quadrature Domains: Basic Properties, 1.
Quadrature Domains: Basic Properties, 2.
Schwarzian Reflection, Revisited.
Projectors from L? (dOmega) to H? (dOmega).
The Friedrichs Operator.
Concluding Remarks.
Bibliography.
Index.
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Harold S. Shapiro Royal Institute of Technology, Stockholm, Sweden.
Note: Product cover images may vary from those shown
