This volume consists of the proceedings of the NATO Advanced Research Workshop on Approximation by Solutions of Partial Differential Equations, Quadrature Formulae, and Related Topics, which was held at Hanstholm, Denmark.
These proceedings include the main invited talks and contributed papers given during the workshop. The aim of these lectures was to present a selection of results of the latest research in the field. In addition to covering topics in approximation by solutions of partial differential equations and quadrature formulae, this volume is also concerned with related areas, such as Gaussian quadratures, the Pompelu problem, rational approximation to the Fresnel integral, boundary correspondence of univalent harmonic mappings, the application of the Hilbert transform in two dimensional aerodynamics, finely open sets in the limit set of a finitely generated Kleinian group, scattering theory, harmonic and maximal measures for rational functions and the solution of the classical Dirichlet problem. In addition, this volume includes some problems in potential theory which were presented in the Problem Session at Hanstholm.
Characterizations of balls and strips via harmonic quadrature; better than uniform approximation on closed sets by harmonic functions with singularities and applications; uniform approximation by flobal harmonic functions; weighted Lp approximation by holomorphic functions; boundary correspondence of univalent harmonic mappings from the unit disc onto a Jordan domain; finely open sets in the limit set of a finitely generated Kleinian group; rational approximation to the Fresnel integral; axiomatic approximation; characterization of open strips by harmonic quadrature; mean value theorems and best L1- approximation; mapping properties of the wave operators in scattering theory; harmonicity modules and applications to the approximation by polyharmonic functions; a comparison of harmonic and maximal measures for rational functions; the role of the Hilbert transform in 2-dimensional aerodynamics; approximation by harmonic functions and the Dirichlet problem; on the existance-problem for Gauss-quadrature on the sphere; a bibliographic survey of the Pompeiu problem; problems.