Multivariate Approximation Theory IV

1. Front Matter

   Pages I-IX

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2. A Recursion Formula for the Dimension of Super Spline Spaces of Smoothness r and Degree d > r2^k

   • 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

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.

• Calculation
• Invariant
• algebra
• function
• recursion
• variable

• 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

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