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Algebraic properties of discrete box splines

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Abstract

The central objective of this paper is to discuss linear independence of translates of discrete box splines which we introduced earlier as a device for the fast computation of multivariate splines. The results obtained here allow us to draw conclusions about the structure of such discrete splines which have, in particular, applications to counting the number of nonnegative integer solutions of linear diophantine equations.

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Authors and Affiliations

  1. Fakultät für Mathematik, Universität Bielefeld, 4800, Bielefeld 1, F.R.G.

    Wolfgang Dahmen

  2. Department of Mathematical Sciences, IBM T. J. Watson Research Center, P.O. Box 218, 10598, Yorktown Heights, New York, USA

    Charles A. Micchelli

Authors
  1. Wolfgang Dahmen
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  2. Charles A. Micchelli
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Additional information

Communicated by Klaus Höllig.

Dedicated to I. J. Schoenberg on the occasion of his eighty-fourth birthday

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Dahmen, W., Micchelli, C.A. Algebraic properties of discrete box splines. Constr. Approx 3, 209–221 (1987). https://doi.org/10.1007/BF01890565

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  • DOI: https://doi.org/10.1007/BF01890565

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