The Schwarz Function and Its Generalization to Higher Dimensions
The University of Arkansas Lecture Notes in the Mathematical Sciences
1. Auflage April 1992
128 Seiten, Hardcover
Wiley & Sons Ltd
ISBN:
978-0-471-57127-8
John Wiley & Sons
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.
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.
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.
