Recent Progress in Multivariate Approximation

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These proceedings capture key topics and results from the Fourth International Conference on Multivariate Approximation, held from September 24-29, 2000, at the University of Dortmund's guest-house, Haus Bommerholz. The conference brought together 43 participants from 16 countries, featuring 9 invited lectures, 21 contributed talks, and two problem sessions. The articles included are peer-refereed and edited for publication. Continuing the tradition of this conference series, the event focused on advancing specific areas of Multivariate Approximation Theory. Topics discussed encompassed approximation on compact sets (spheres, balls, compact homogeneous manifolds), spherical designs, energy functionals, interpolation using radial basis functions and splines, frame theory, Gabor analysis, refinable function systems, subdivision, as well as properties of harmonic, polyharmonic, and blending functions, along with sampling and data compression. The editors extend their gratitude to all who supported the conference and the preparation of this volume, particularly the Deutsche Forschungsgemeinschaft for funding, the University of Dortmund, the staff of Haus Bommerholz for their assistance, and the Universities of Dortmund and Duisburg for their financial contributions to this proceedings volume.