ENGLISH

The Schwarz Function and Its Generalization to Higher Dimensions

By Harold S. Shapiro

Book information

Publisher
John Wiley & Sons;Wiley Interscience
Year
1992
ISBN
0-471-57127-X, 9780471571278
Language
english
Format
DJVU
Filesize
1 MB (1415143 bytes)
Series
University of Arkansas Lecture Notes in the Mathematical Sciences Vol. 9
Edition
1
Pages
128\125
Library
kolxoz
Time added
2017-10-15 16:00:00

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 Content: 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 L2 ( OMEGA) to H2 ( OMEGA). The Friedrichs Operator. Concluding Remarks. Bibliography. Index.

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