Ebook: Recent Progress in Multivariate Approximation: 4th International Conference, Witten-Bommerholz (Germany), September 2000

These proceedings contain the main topics and results presented at the Fourth International Conference on Multivariate Approximation. The meeting took place during the week of September 24-29, 2000 at the now well-known "Haus Bommerholz", the guest-house of the University of Dortmund. It hosted 43 participants from 16 countries, and the program included 9 invited one-hour lectures, 21 contributed talks, and two problem sessions. The articles collected here are carefully peer-refereed and suitably edited for publication. Following the tradition of this series of conferences, the meeting was aimed at advancing selected topics of Multivariate Approximation Theory. These include approximation on compact sets (such as spheres, balls, or compact ho­ mogeneous manifolds), spherical designs and energy functionals, interpolation by radial basis functions and by splines, frame theory and Gabor analysis, re­ finable function systems and subdivision, properties of harmonic, polyharmonic and blending functions, sampling and data compression, among others. The editors would like to express their thanks to all who have given their sup­ port to the conference, and to the preparation of this book. In particular, our thanks go to the Deutsche Forschungsgemeinschaft for their funding of the con­ ference, to the University of Dortmund, and to the staff of Haus Bommerholz for their help running the conference, and to the Universities of Dortmund and Duisburg for the financial support of this proceedings volume.

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Content:
Front Matter....Pages 1-18
Jochen W. Schmidt in Memoriam....Pages 19-21
Best Approximation of Polynomials on the Sphere and on the Ball....Pages 23-30
The Sign of a Harmonic Function Near a Zero....Pages 31-32
Radial Basis Functions for the Sphere....Pages 33-47
Cubature Formulae for Polyharmonic Functions....Pages 49-74
On the Structure of Kergin Interpolation for Points in General Position....Pages 75-87
Frames Containing a Riesz Basis and Approximation of the Inverse Frame Operator....Pages 89-100
Kronecker Type Convolution of Function Vectors with one Refinable Factor....Pages 101-113
Open Problem: Existence of Hermite Interpolatory Subdivision Schemes with Arbitrary Large Smoothnesses....Pages 115-134
Asymptotic Formulas in Cardinal Interpolation and Orthogonal Projection....Pages 135-137
Some Cubature Formulae Using Mixed Type Data....Pages 139-157
On an Extremal Problem Originating in Questions of Unconditional Convergence....Pages 159-162
Node Insertion and Node Deletion for Radial Basis Functions....Pages 163-184
Tangent Space Methods for Approximation on Compact Homogeneous Manifolds....Pages 185-192
Open Problem Concerning Fourier Transforms of Radial Functions in Euclidean Space and on Spheres....Pages 193-209
Local Lagrange Interpolation on Powell-Sabin Triangulations and Terrain Modelling....Pages 211-224
The Geometry of Nodes in a Positive Quadrature on the Sphere....Pages 225-226
Normalized Tight Frames in Finite Dimensions....Pages 227-244
Publication of Jochen W. Schmidt....Pages 245-248
....Pages 249-252