Constructive Approximation

, Volume 3, Issue 1, pp 199–208 | Cite as

The polynomials in the linear span of integer translates of a compactly supported function

  • Carl de Boor
Article

Abstract

Algebraic facts about the space of polynomials contained in the span of integer translates of a compactly supported function are derived and then used in a discussion of the various quasi-interpolants from that span.

Key words and phrases

Box splines Multivariate Splines Quasi-interpolant Semidiscrete convolution 

AMS classification

41A15 41A63 41A25 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. BH.
    C. de Boor, K. Höllig (1982/83):B-splines from parallelepipeds. J. Analyse Math.,42:99–115.Google Scholar
  2. BJ.
    C. de Boor, R.-Q. Jia (1985):Controlled approximation and a characterization of the local approximation order. Proc. Amer. Math. Soc.,95:547–553.Google Scholar
  3. CD.
    C. K. Chui, H. Diamond (1985): A natural formulation of quasi-interpolation by multivariate splines. CAT Report No. 103. College Station: Texas A&M University.Google Scholar
  4. CJW.
    C. K. Chui, K. Jetter, J. D. Ward (1985): Cardinal interpolation by multivariate splines, CAT Report No. 86. College Station: Texas A&M University.Google Scholar
  5. CL.
    C. K. Chui, M. J. Lai (1985): A multivariate analog of Marsden's identity and a quasiinterpolation scheme. CAT Report No. 88. College Station: Texas A&M University.Google Scholar
  6. DM83.
    W. Dahmen, C. A. Micchelli (1983):Translates of multivariate splines. Linear Algebra Appl.,52/3:217–234.Google Scholar
  7. DM85.
    W. Dahmen, C. A. Micchelli (1985):On the solution of certain systems of partial difference equations and linear independence of translates of box splines. Trans. Amer. Math. Soc.,292:305–320.Google Scholar
  8. FS.
    G. Fix, G. Strang (1969):Fourier analysis of the finite element method in Ritz-Galerkin theory. Studies Appl. Math.,48:265–273.Google Scholar
  9. S.
    I. J. Schoenberg (1946):Contributions to the problem of approximation of equidistant data by analytic functions, Parts A and B. Quart. Appl. Math.,IV: 45–99, 112–141.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1987

Authors and Affiliations

  • Carl de Boor
    • 1
  1. 1.Mathematics Research CenterMadisonUSA

Personalised recommendations