## Advanced Problems in Constructive Approximation: 3rd International Dortmund Meeting on Approximation Theory (IDoMAT) 2001Martin D. Buhmann, Detlef Mache 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. |

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### Contents

Linear Perturbations of the Classical Orthogonal Polynomials which are Eigen functions of Linear Differential Operators | 1 |

A General Method for Regularity | 21 |

De la Vallee Poussin Means for the Hankel Transform | 27 |

Polynomial Bases on the Sphere | 39 |

A Shooting Method for Symbolic Computation of Splines | 53 |

Error Estimates for the CaratheodoryFejer Method in Polynomial Approximation | 63 |

Shape Preserving Widths of Weighted SobolevType Classes | 79 |

95 | |

Semigroups Associated to Mache Operators | 143 |

A Survey on Lagrange Interpolation Based on Equally Spaced Nodes | 153 |

Multiresolution Analysis with Pulses | 165 |

Hsplines and Quasiinterpolants on a Three Directional Mesh | 187 |

Approximation by Positive Definite Kernels | 203 |

Inequalities for Polynomials With Weights Having Infinitely many Zeros on the Real Line | 223 |

Some Erdostype Convergence Processes in Weighted Interpolation | 237 |

Absolute Continuity of Spectral Measure for Certain Unbounded Jacobi Matrices | 255 |

Curious qSeries as Counterexamples in Pade Approximation | 109 |

On the Degree of Approximation in Multivariate Weighted Approximation | 129 |

Approximation on Compact Subsets of R | 263 |

### Other editions - View all

Advanced Problems in Constructive Approximation: 3rd International Dortmund ... Martin D. Buhmann,Detlef Mache No preview available - 2003 |

Advanced Problems in Constructive Approximation: 3rd International Dortmund ... Martin D. Buhmann,Detlef Mache No preview available - 2003 |

### Common terms and phrases

2002 Birkhauser Verlag analysis Approx approximation theory Bavinck Bernstein Birkhauser Verlag Basel box-splines Buhmann and D.H. Caratheodory-Fejer Chebyshev coefficients computation constant Constructive Approximation Eds continued fraction convergence D.H. Mache International decomposition defined denote differential equations differential operator Dortmund e-mail eigenfunctions estimate example Fejer Fejer kernel finite formula Fourier Freud weights given Hankel transform impulse inequality inner product integer Jacobi Jacobi polynomials Koekoek Lagrange interpolation Laguerre Laguerre polynomials Lemma LnUn M.D. Buhmann Mache International Series Math Mathematik matrix Meixner polynomials multiresolution analysis n-width native space nodes norm numbers Numerical Mathematics Vol orthogonal polynomials Pade Approximants Pal-type interpolation polynomials as eigenfunctions positive definite power series proof properties prove quasi-interpolants result root of unity satisfying semigroup Series of Numerical smooth Sobolev type spline subsets symmetric Theorem 2.1 unit ball UnLn values vectors Verlag Basel ISBN wavelet weight function zeroes