Schwarz Function and Its Generalization to Higher Dimensions

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.

• 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.