Classical and Modern Potential Theory and Applications

A NATO Advanced Research Workshop on Classical and Modern Potential The ory and Applications was held at the Chateau de Bonas, France, during the last week of July 1993. The workshop was organized by the Co-Directors M. Goldstein (Ari zona) and K. GowriSankaran (Montreal). The other members of the organizing committee were J. Bliedtner (Frankfurt), D. Feyel (Paris), W. K. Hayman (York, England) and I. Netuka (Praha). The objective of the workshop was to bring to gether the researchers at the forefront of the aspects of the Potential Theory for a meaningful dialogue and for positive interaction amongst the mathematicians prac tising different aspects of the theory and its applications. Fifty one mathematicians participated in the workshop. The workshop covered a fair representation of the classical aspects of the theory covering topics such as approximations, radial be haviour, value distributions of meromorphic functions and the modern Potential theory including axiomatic developments, probabilistic theories, studies on infinite dimensional Wiener spaces, solutions of powers of Laplacian and other second order partial differential equations. There were keynote addresses delivered by D. Armitage (Belfast), N. Bouleau (Paris), A. Eremenko (Purdue), S. J. Gardiner (Dublin), W. Hansen (Bielefeld), W. Hengartner (Laval U. , Quebec), K. Janssen (Dusseldorf), T. Murai (Nagoya), A. de la Pradelle (Paris) and J. M. Wu (Urbana). There were thirty six other invited talks of one half hour duration each.

Klappentext

A NATO Advanced Research Workshop on Classical and Modern Potential The ory and Applications was held at the Chateau de Bonas, France, during the last week of July 1993. The workshop was organized by the Co-Directors M. Goldstein (Ari zona) and K. GowriSankaran (Montreal). The other members of the organizing committee were J. Bliedtner (Frankfurt), D. Feyel (Paris), W. K. Hayman (York, England) and I. Netuka (Praha). The objective of the workshop was to bring to gether the researchers at the forefront of the aspects of the Potential Theory for a meaningful dialogue and for positive interaction amongst the mathematicians prac tising different aspects of the theory and its applications. Fifty one mathematicians participated in the workshop. The workshop covered a fair representation of the classical aspects of the theory covering topics such as approximations, radial be haviour, value distributions of meromorphic functions and the modern Potential theory including axiomatic developments, probabilistic theories, studies on infinite dimensional Wiener spaces, solutions of powers of Laplacian and other second order partial differential equations. There were keynote addresses delivered by D. Armitage (Belfast), N. Bouleau (Paris), A. Eremenko (Purdue), S. J. Gardiner (Dublin), W. Hansen (Bielefeld), W. Hengartner (Laval U. , Quebec), K. Janssen (Dusseldorf), T. Murai (Nagoya), A. de la Pradelle (Paris) and J. M. Wu (Urbana). There were thirty six other invited talks of one half hour duration each.

Inhalt
Nonlinear PDE and the Wiener Test.- k-Superharmonic Functions and L.Kelvin's Theorem.- On the Invariance of the Solutions of the Weinstein Equation under Möbius Transformations.- Radial Limiting Behaviour of Harmonic and Superharmonic Functions.- Multiparameter Processes associated with Ornstein-Uhlenbeck Semi-groups.- On the Problem of Hypoellipticity on the Infinite Dimensional Torus.- L'équation de Monge-Ampère dans un espace de Banach.- Excessive Functions and Excessive Measures. Hunt's Theorem on Balayages, Quasi-continuity.- The Wiener Test for Poincaré-Dirichlet Forms.- The Best Approach for Boundary Limits.- Fine Behaviour of Balayages in Potential Theory.- Some Results about Sequential Integration on Wiener Space.- Schwarz Lemma type Inequalities for Harmonic Functions in the Ball.- Duality of H-Cones.- Régularité et Intégrabilité des Fonctionnelles de Wiener.- Poincaré Inequalities in L1-norm for the Sphere and a Strong Isoperimetric Inequality in R1.- Uniform and Tangential Harmonic Approximation.- Inversion and Reflecting Brownian Moti.- ?-Potentials.- Fatou-Doob Limits and the Best Filters.- Gaussian Upper Bounds for the Heat Kernel and its Derivatives on a Riemannian Manifold.- Integrals of Analytic Functions along 2 Curves.- On the Restricted Mean Value Property for Measurable Functions.- A Constructive Method for Univalent Logharmonic Mappings.- Choquet Type Integral Representation of Polyexcessive Functions.- Refining the Local Uniform Convergence Topology.- Daily Rheological Phenomena.- Convergence Property and Superharmonic Functions on Balayage Spaces.- Mean Value Property of Harmonic Functions.- Farrell and Mergelyan Sets for the Space of Bounded Harmonic Functions.- Mèthodes Analytiques en Dimension Infinie.- Construction d'unProcessus à deux Parametres à partir d'un Semi-groupe à un Paramètre.- Capacities and Harmonic Measures for Uniformly Elliptic Operators of non-Divergence Form.- Problems.