The Schwarz Function and Its Generalization to Higher Dimensions / Edition 1

by Harold S. Shapiro

Overview

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.

Product Details

ISBN-13:	9780471571278
Publisher:	Wiley
Publication date:	04/16/1992
Series:	The University of Arkansas Lecture Notes in the Mathematical Sciences , #4
Pages:	128
Product dimensions:	6.30(w) x 9.45(h) x 0.59(d)

About the Author

Harold Seymour Shapiro is a professor emeritus of mathematics at the Royal Institute of Technology in Stockholm, Sweden, best known for inventing the so-called Shapiro polynomials also known as Golay-Shapiro polynomials or Rudin-Shapiro polynomials and for pioneering work on quadrature domains.

Table of Contents

The Schwarz Principle of Reflection.

The Logarithmic Potential, Balayage, and Quadrature Domains.

Examples of &‘grave;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.

Editorial Reviews

Expanded from a series of five lectures to an audience of classical function theorists at a conference in Fayetteville, Florida, April 1988. Discusses the Schwartz function in a treatment that combines classical complex analysis and potential theory, with the modern theory of distributions and partial differential equations. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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