Complex Potential Theory

by Paul M. Gauthier (Editor)

Overview

In Complex Potential Theory, specialists in several complex variables meet with specialists in potential theory to demonstrate the interface and interconnections between their two fields. The following topics are discussed:

• Real and complex potential theory. Capacity and approximation, basic properties of plurisubharmonic functions and methods to manipulate their singularities and study theory growth, Green functions, Chebyshev-like quadratures, electrostatic fields and potentials, propagation of smallness.
• Complex dynamics. Review of complex dynamics in one variable, Julia sets, Fatou sets, background in several variables, Hénon maps, ergodicity use of potential theory and multifunctions.
• Banach algebras and infinite dimensional holomorphy. Analytic multifunctions, spectral theory, analytic functions on a Banach space, semigroups of holomorphic isometries, Pick interpolation on uniform algebras and von Neumann inequalities for operators on a Hilbert space.

Product Details

ISBN-13:	9780792330059
Publisher:	Springer-Verlag New York, LLC
Publication date:	07/31/1994
Series:	NATO Science Series C: (closed) Series , #439
Pages:	576
Product dimensions:	6.14(w) x 9.21(h) x 1.25(d)

Table of Contents

Analytic multifunctions and their applications.- Harmonic approximation on closed subsets of Riemannian manifolds.- Pick interpolation, Von Neumann inequalities, and hyperconvex sets.- Complex dynamics in higher dimensions.- Analytic functions on Banach spaces.- Uniform approximation.- Plurisubharmonic functions and their singularities.- Chebyshev-type quadratures: use of complex analysis and potential theory.- General aspects of potential theory with respect to problems of differential equations.- Removability, capacity and approximation.- Semigroups of holomorphic isometries.

Editorial Reviews

Proceedings of the NATO Advanced Study Institute held in Montreal, Canada, July-August 1993, to bring together specialists in several complex variables (many of whom have contributed to complex potential theory) and specialists in potential theory (all of whom have contributed to several complex variables) together with young researchers and graduate students for an interchange of ideas and techniques. Not only is the status of current research presented, but also the relevant background, much of which was not previously available in books. The following topics and their interconnections are discussed: real and complex potential theory; complex dynamics; and Banach algebras and infinite dimensional holomorphy. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Booknews

‘The proceedings are recommended for those who are interested in complex function theory, potential theory, interpolation and approximation theory and related domains.'
Acta Sci. Mathematica (1995)

From the Publisher