The current form of modern approximation theory is shaped by many new de velopments which are the subject of this series of conferences. The International Meetings on Approximation Theory attempt to keep track in particular of fun damental advances in the theory of function approximation, for example by (or thogonal) polynomials, (weighted) interpolation, multivariate quasi-interpolation, splines, radial basis functions and several others. This includes both approxima tion order and error estimates, as well as constructions of function systems for approximation of functions on Euclidean spaces and spheres. It is a piece of very good fortune that at all of the IDoMAT meetings, col leagues and friends from all over Europe, and indeed some count ries outside Europe and as far away as China, New Zealand, South Africa and U.S.A. came and dis cussed mathematics at IDoMAT conference facility in Witten-Bommerholz. The conference was, as always, held in a friendly and congenial atmosphere. After each meeting, the delegat es were invited to contribute to the proceed ing's volume, the previous one being published in the same Birkhäuser series as this one. The editors were pleased about the quality of the contributions which could be solicited for the book. They are refereed and we should mention our gratitude to the referees and their work.

State of the art in and applications of approximation theory

Klappentext

The current form of modern approximation theory is shaped by many new de­ velopments which are the subject of this series of conferences. The International Meetings on Approximation Theory attempt to keep track in particular of fun­ damental advances in the theory of function approximation, for example by (or­ thogonal) polynomials, (weighted) interpolation, multivariate quasi-interpolation, splines, radial basis functions and several others. This includes both approxima­ tion order and error estimates, as well as constructions of function systems for approximation of functions on Euclidean spaces and spheres. It is a piece of very good fortune that at all of the IDoMAT meetings, col­ leagues and friends from all over Europe, and indeed some count ries outside Europe and as far away as China, New Zealand, South Africa and U.S.A. came and dis­ cussed mathematics at IDoMAT conference facility in Witten-Bommerholz. The conference was, as always, held in a friendly and congenial atmosphere. After each meeting, the delegat es were invited to contribute to the proceed­ ing's volume, the previous one being published in the same Birkhäuser series as this one. The editors were pleased about the quality of the contributions which could be solicited for the book. They are refereed and we should mention our gratitude to the referees and their work.

Inhalt
Linear Perturbations of the Classical Orthogonal Polynomials which are Eigenfunctions of Linear Differential Operators.- (0, 1) Pál-type Interpolation: A General Method for Regularity.- De la Vallée Poussin Means for the Hankel Transform.- Polynomial Bases on the Sphere.- A Shooting Method for Symbolic Computation of Splines.- Error Estimates for the Caratheodory-Fejér Method in Polynomial Approximation.- Shape Preserving Widths of Weighted Sobolev-Type Classes.- On Approximation Methods by Using Orthogonal Polynomial Expansions.- Curious q-Series as Counterexamples in Padé Approximation.- On the Degree of Approximation in Multivariate Weighted Approximation.- Semigroups Associated to Mache Operators.- A Survey on Lagrange Interpolation Based on Equally Spaced Nodes.- Multiresolution Analysis with Pulses.- H-Splines and Quasi-interpolants on a Three Directional Mesh.- Approximation by Positive Definite Kernels.- Inequalities for Polynomials With Weights Having Infinitely many Zeros on the Real Line.- Some Erd?s-type Convergence Processes in Weighted Interpolation.- Absolute Continuity of Spectral Measure for Certain Unbounded Jacobi Matrices.- Approximation on Compact Subsets of R.