Approximation by Solutions of Partial Differential Equations

✍ Scribed by D. H. Armitage (auth.), B. Fuglede, M. Goldstein, W. Haussmann, W. K. Hayman, L. Rogge (eds.)

• Publisher: Springer Netherlands
• Year: 1992
• Tongue: English
• Leaves: 206
• Series: NATO ASI Series 365
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xii
Characterizations of Balls and Strips via Harmonic Quadrature....Pages 1-9
Better than Uniform Approximation on Closed Sets by Harmonic Functions with Singularities and Applications....Pages 11-14
Uniform Approximation by Global Harmonic Functions....Pages 15-26
Weighted L p Approximation by Holomorphic Functions....Pages 27-49
Boundary Correspondence of Univalent Harmonic Mappings from the Unit Disc onto a Jordan Domain....Pages 51-60
Finely Open Sets in the Limit Set of a Finitely Generated Kleinian Group....Pages 61-67
Rational Approximation to the Fresnel Integral....Pages 69-77
Axiomatic Approximation....Pages 79-85
Characterization of Open Strips by Harmonic Quadrature....Pages 87-92
Mean Value Theorems and Best L 1 -Approximation....Pages 93-102
Mapping Properties of the Wave Operators in Scattering Theory....Pages 103-110
Harmonicity Modulus and Applications to the Approximation by Polyharmonic Functions....Pages 111-125
A Comparison of Harmonic and Maximal Measures for Rational Functions....Pages 127-139
The Role of the Hilbert Transform in 2-Dimensional Aerodynamics....Pages 141-154
Approximation by Harmonic Functions and the Dirichlet Problem....Pages 155-168
On the Existence-Problem for Gauss-Quadrature on the Sphere....Pages 169-184
A Bibliographic Survey of the Pompeiu Problem....Pages 185-194
Problems....Pages 195-201

✦ Subjects

Potential Theory; Approximations and Expansions; Partial Differential Equations