Complex Potential Theory

**`**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)** 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. Front Matter....Pages i-xix Analytic multifunctions and their applications....Pages 1-74 Harmonic approximation on closed subsets of Riemannian manifolds....Pages 75-87 Pick interpolation, Von Neumann inequalities, and hyperconvex sets....Pages 89-129 Complex dynamics in higher dimensions....Pages 131-186 Analytic functions on Banach spaces....Pages 187-233 Uniform approximation....Pages 235-271 Plurisubharmonic functions and their singularities....Pages 273-323 Chebyshev-type quadratures: use of complex analysis and potential theory....Pages 325-364 General aspects of potential theory with respect to problems of differential equations....Pages 365-418 Removability, capacity and approximation....Pages 419-473 Semigroups of holomorphic isometries....Pages 475-548 Back Matter....Pages 549-552 ` 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) Proceedings of the NATO Advanced Study Institute and Séminaire de mathématiques supérieures, Montréal, Canada, July 26--August 6, 1993