The Schwarz Function and Its Generalization to Higher Dimensions

Harold S. Shapiro (Author)

9780471571278, Wiley

Hardback, published 14 April 1992

128 pages
24 x 16 x 1.5 cm, 0.369 kg

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.

Subject Areas: Mathematics [PB]