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The Schwarz Function and Its Generalization to Higher Dimensions

The Schwarz Function and Its Generalization to Higher Dimensions

Harold S. Shapiro

ISBN: 978-0-471-57127-8

Mar 1992

128 pages

Select type: Hardcover

In Stock

$266.95

Description

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.
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.