Advances in
Multivariate Approximation
1998
Wiley-VCH

edited by

Werner Haußmann,
Universität Duisburg
Kurt Jetter,
Universität Hohenheim
Manfred Reimer,
Universität Dortmund

Contents of Web Page:

• Preface
• Acknowledgement
• Table of Contents
• Participants
• Scientific Programm of the conference
• Contacting the Editors

Preface

The Third International Conference on Multivariate Approximation at ``Haus Bommerholz'', the guest-house of the University of Dortmund, took place during the week of September 27 through October 2, 1998. It was attended by 50 participants from 18 countries. The program included 10 invited lectures, 25 contributed talks, and two problem sessions. In these Proceedings we collect most of the lectures, suitably prepared by the authors for publication, and carefully peer-refereed.
As was the case for the preceding conferences, the meeting was intended to advance several selected topics from modern aspects of Multivariate Approximation Theory. This time, emphasis was put on the following subjects: Interpolation and Approximation on Spheres and Balls, Approximation by Solutions of Partial Differential Equations, Construction of Node Systems, and Scattered Data Techniques. Leading experts in these areas and quite a number of young researchers made the meeting a stimulating event, with lively discussions and scientific interactions to support and initiate future research.
The editors are grateful to all who have contributed to the success of the conference and to the production of this Proceedings volume. In particular, our thanks go to the Deutsche Forschungsgemeinschaft whose funding made the conference possible, and to the Ministerium für Schule, Weiterbildung, Wissenschaft und Forschung of the Land Nordrhein-Westfalen for sponsoring this volume. We acknowledge the help of the authors and the referees to guarantee publications of high scientific standard, and we thank the WILEY-VCH publishers for their kind cooperation. In addition, we acknowledge the extensive help of Dr. Hermann Hoch and Dipl.-Math. Jörg Zabold (Duisburg) during the production of this Proceedings volume. Finally, we would especially like to thank the conference secretary, Mrs. Lamprecht, and the staff of Haus Bommerholz, for all their help.
May 1, 1999
Werner Haußmann
Kurt Jetter
Manfred Reimer

Acknowledgement

                Deutsche Forschungsgemeinschaft (DFG)

whose funding made the conference possible.

The production of this volume was sponsored by the

                Ministerium für Schule und Weiterbildung,

                Wissenschaft und Forschung

                des Landes Nordrhein-Westfalen.

We are grateful for the generous support.

The Editors

Table of Contents

Participants 9
Scientific Program of the Conference 15
Problems of Approximation Theory in Discrete Geometry N. N. Andreev and V. A. Yudin 19
Dense Vector Spaces of Universal Harmonic Functions D. H. Armitage 33
Best One-sided Subharmonic Functions D. H. Armitage and S. J. Gardiner 43
Numerical Stability of Fast Fourier TransformsG. Baszenski, R. Xuefang and M. Tasche 57
The Saturation Theorem for Box Spline Orthogonal ProjectionM. Beska and K. Dziedziul 73
Problem on Monotonic Behaviour of Bernstein OperatorsM. Beska and K. Dziedziul 84
Best One-Sided-Approximation by Blending Functions B. D. Bojanov, D. P. Dryanov,W. Haußmann and G. P. Nikolov 85
On the Asymptotics of Points which Maximize Determinants of the Form L. Bos and U. Maier 107
Besov Regularity for the Stokes Problem F.-J. Delvos 139
Multiscale Modelling from Geopotential DataW. Freeden, O. Glockner and R. Litzenberger 151
On a Family of Orthogonal Wavelets on the Quincunx Grid: Open Regularity QuestionsA. Gottscheber and G. Steidl 175
Average Case Analysis of Numerical Integration P. J. Grabner, P. Liardet and R. F. Tichy 185
Cubature Formulas on SpheresH. König 201
Numerical Calculation of Spherical DesignsU. Maier 213
On Bivariate Spline SpacesG. Nürnberger and F. Zeilfelder 227
Spherical Polynomial Approximations: A SurveyM. Reimer 231
Range Restricted Interpolation by Cubic-Splines on Clough-Tocher J. W. Schmidt 253
Some Error Estimates for Periodic Interpolation of Functions from Besov SpacesW. Sickel and F. Sprengel 269
The Uniform Error of Hyperinterpolation on the Sphere I. H. Sloan and R. S. Womersley 289
Simultaneous Approximation in the Dirichlet SpaceA. Stray 307
The Equivalence between Weighted Moduli of Smoothness on a Simplex and their ApplicationsP.-C. Xuan 321