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Full Description
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, Henon 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.
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.
