The Schwarz function and its generalization to higher dimensions
著者
書誌事項
The Schwarz function and its generalization to higher dimensions
（University of Arkansas lecture notes in the mathematical sciences, v. 9）
Wiley, c1992
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注記
An expanded version of a series of lectures delivered at a conference at the University of Arkansas in April 1988
"A Wiley-Interscience publication."
Bibliographical references: p. [97]-103
Includes index
内容説明・目次
内容説明
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.
目次
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.
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