Potential Theory - ICPT 94

Proceedings of the International Conference on Potential Theory held in Kouty, Czech Republic, August 13-20, 1994

Editors Josef Krai Jaroslav Lukes Ivan Netuka Jifi Vesely

w DE G Walter de Gruyter • Berlin • New York 1996 Contents

Preface v

Invited Lectures

Heinz BAUER Recollections, reflections, results — Introductory thoughts to the ICPT 94 1

Nicolas BOULEAU Constructions of Dirichlet structures 9

Gustave CHOQUET Les processus mentaux de la creation 27

Stephen J. GARDINER Harmonic approximation 51

Wolfhard HANSEN Restricted mean value property and harmonic functions 67

Victor P. HAVIN Approximation properties of harmonic vector fields and differential forms 91

Jan MALY Nonlinear potentials and quasilinear PDE's 103

Pertti MATTILA Removability, geometric measure theory, and singular integrals 129

Jozef SICIAK Bernstein-Walsh type theorems for pluriharmonic functions 147

Gregory C. VERCHOTA Potentials for the Dirichlet problem in Lipschitz domains 167

Wolfgang WOESS Dirichlet problem at infinity for harmonic functions on graphs 189 vm Contributed Papers

Hiroaki AIKAWA and Alexandr A. BORICHEV Quasiadditivity and measure property of capacity and the tangential boundary behavior of harmonic functions 219

David H. ARMITAGE The Riesz-Herglotz representation for positive harmonic functions via Choquet's theorem 229

Zouhir BEN NAHIA and Nejib BEN SALEM Spherical harmonics and applications associated with the Weinstein operator 233

Zouhir BEN NAHIA and Nejib BEN SALEM On a mean value property associated with the Weinstein operator 243

Lucian BEZNEA and Nicu BOBOC Once more about the semipolar sets and regular excessive functions 255

Mounir BEZZARGA and Gheorghe BUCUR Duality for semi-dynamical systems 275

Anders BJORN Removable singularities for Hardy spaces in subdomains of C 287

Jurgen BLIEDTNER Approximation by harmonic functions 297

Jurgen BLIEDTNER and Peter A. LOEB Generalized radial limits and the best approach to boundaries 303

Nicu BOBOC and Gheorghe BUCUR Dilation operators in excessive structures; existence and uniqueness 311

Miroslav BRZEZINA and Martina SIMUNKOVA On the harmonic morphism for the Kolmogorov type operators 341

Mohamed HMISSI Potentiels et attracteurs d'un systeme dynamique 359

Niels JACOB Various approaches to the Dirichlet problem for non-local operators satisfying the positive maximum principle 367 IX

Pawel KROGER Estimates for eigenvalues of the Laplacian 377

Visa LATVALA Fine A-super solutions and finely A-superharmonic functions 383

Heinz LEUTWILER Remarks on modified Clifford analysis 389

Peter V. MALYSHEV and Dmitry V. MALYSHEV Electric fields in domains with complicated structure 399

Volker METZ Renormalization on fractals 413

Charles N. MOORE Estimates for the density of the area integral 423

Eugen POPA and Liliana POPA Tensor product of standard H-cones and duality 433

Pavel PYRIH An example of packing related small sets 443

Rene L. SCHILLING On the domain of the generator of a subordinate semigroup 449

Hisako WATANABE The double layer potentials for a bounded domain with fractal boundary 463

Problems 473

Appendices

List of lectures 489

List of participants 493