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Multivariate Approximation Theory IV

Proceedings of the Conference at the Mathematical Research Institute at Oberwolfach, Black Forest, February 12–18, 1989

  • Conference proceedings
  • © 1989

Overview

Authors:
  1. C. K. Chui

    1. Center for Approximation Theory Department of Mathematics, Texas A & M University, College Station, USA

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  2. W. Schempp

    1. Lehrstuhl für Mathematik I, Universität Siegen, Siegen, Germany

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  3. K. Zeller

    1. Mathematisches Institut, Universität Tübingen, Tübingen 1, Germany

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Part of the book series: International Series of Numerical Mathematics (ISNM, volume 90)

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Table of contents (37 papers)

  1. Front Matter

    Pages I-IX
    Download chapter PDF

  2. A Recursion Formula for the Dimension of Super Spline Spaces of Smoothness r and Degree d > r2k

    • Peter Alfeld, Maritza Sirvent
    Pages 1-8

  3. Approximation with Barycentric Coordinates the Hilbertian Case

    • M. Atteia
    Pages 9-14

  4. A Discrete Fourier Transform Scheme for Boolean Sums of Trigonometric Operators

    • Günter Baszenski, F.-J. Delvos
    Pages 15-24

  5. A Local Basis for Certain Smooth Bivariate PP Spaces

    • Carl de Boor
    Pages 25-30

  6. Polynomial Ideals and Multivariate Splines

    • Carl de Boor, Amos Ron
    Pages 31-40

  7. Cardinal Interpolation with Radial Basis Functions: An Integral Transform Approach

    • M. D. Buhmann
    Pages 41-64

  8. On the Evaluation of Multivariate Lagrange Formulae

    • Jesús M. Carnicer, Mariano Gasca
    Pages 65-72

  9. Asymptotically Optimal Sampling Schemes for Periodic Functions II: The Multivariate Case

    • Han-lin Chen, Charles K. Chui, Charles A. Micchelli
    Pages 73-86

  10. Generalized Bochner-Riesz Means of Fourier Integrals

    • Tianping Chen
    Pages 87-94

  11. An Algorithm for Best Approximating Algebraic Polynomials in L p Over a Simplex

    • Z. Ciesielski
    Pages 95-102

  12. Rational and Algebraic Approximation for Initial- and Boundary-Value-Problems

    • Lothar Collatz
    Pages 103-106

  13. R-th Order Blending Rectangle Rules

    • Franz-Jürgen Delvos
    Pages 107-114

  14. A Trivariate Boolean Cubature Scheme

    • Franz-Jürgen Delvos, Helmut Nienhaus
    Pages 115-122

  15. Multivariate Band-Limited Functions: Sampling Representation and Approximation

    • Dinh-Dung
    Pages 123-134

  16. Multidimensional Irregular Sampling of Band-Limited Functions in Lp-Spaces

    • Hans G. Feichtinger, Karlheinz Gröchenig
    Pages 135-142

  17. L2-Synthesis by Ambiguity Functions

    • Ephraim Feig, Charles A. Micchelli
    Pages 143-156

  18. Vector Spherical Spline Interpolation

    • Willi Freeden, Theo Gervens
    Pages 157-171

  19. Simultaneous Approximation by Generalized n-th Order Blending Operators

    • Heinz H. Gonska
    Pages 173-180

  20. Some Results on Quadratic Splines of Three (and More) Variables

    • Gerhard Heindl
    Pages 181-192
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Keywords

About this book

Multivariate Approximation Theory forms a rapidly evolving field in Applied Mathematics. The reason for its particular current interest lies in its impact on Computer Aided Geometric Design (CAGD), Image Processing, Pattern Recogni tion, and Mult idimensional Signal Processing. Mul ti var iate Bernstein polynomials and box splines, for example, play an important role in CAGD. Conversely, the highly important filter bank design problem of signal processing, for instance, gives rise to a new family of multivariate approximating functions, the Gabor wavelets, with interesting technological and biological applications. The conferences on Multivariate Approximation Theory held at the Mathematical Research Institute at Oberwolfach, Black Forest, in 1976, 1979, 1982, 1985 and 1989 ref lect the progress made in this area and related fie Ids. The present volume which is a continuation of the preceding volumes Constructive Theory of Functions of Several Variables, Lecture Notes in Mathematics 571 (1977) Multivariate Approximation Theory, ISNM 51 (1979) Multivariate Approximation Theory II, ISNM 61 (1982) Multivariate Approximation Theory III, ISNM 75 (1985) is based on the conference held on February 12-18, 1989. It includes most of the lectures presented at the Oberwolfach meeting and reveals the wide spectrum of activities in the field of multivariate approximation. The organizers are grateful to the Director of the Oberwolfach Mathematical Research Institute, Professor Dr. M. Barner, and his staff for providing the facili ties, and to Dr. G. Baszenski, Professor Dr. F. J. Delvos, Dr. H.

Authors and Affiliations

  • Center for Approximation Theory Department of Mathematics, Texas A & M University, College Station, USA

    C. K. Chui

  • Lehrstuhl für Mathematik I, Universität Siegen, Siegen, Germany

    W. Schempp

  • Mathematisches Institut, Universität Tübingen, Tübingen 1, Germany

    K. Zeller

Bibliographic Information

  • Book Title: Multivariate Approximation Theory IV

  • Book Subtitle: Proceedings of the Conference at the Mathematical Research Institute at Oberwolfach, Black Forest, February 12–18, 1989

  • Authors: C. K. Chui, W. Schempp, K. Zeller

  • Series Title: International Series of Numerical Mathematics

  • DOI: https://doi.org/10.1007/978-3-0348-7298-0

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Verlag Basel 1989

  • Hardcover ISBN: 978-3-7643-2384-4Due: 01 October 1989

  • Softcover ISBN: 978-3-0348-7300-0Published: 14 March 2012

  • eBook ISBN: 978-3-0348-7298-0Published: 08 March 2013

  • Series ISSN: 0373-3149

  • Series E-ISSN: 2296-6072

  • Edition Number: 1

  • Number of Pages: IX, 342

  • Topics: Science, Humanities and Social Sciences, multidisciplinary

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