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On Two Polynomial Spaces Associated With a Box Spline

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Author(s)
de Boor, Carl; Dyn, Nira; Ron, Amos
Publisher
University of Wisconsin-Madison Department of Computer Sciences
Citation
TR838
Date
1989
Abstract
The polynomial space H in the span of the integer translates of a box spline M admits a well-known characterization as the joint kernel of a set of homogeneous differential operators with constant coefficients. The dual space H* has a convenient representation by a polynomial space P, explicitly known, which plays an important role in box spline theory as well as in multivariate polynomial interpolation. In this paper we characterize the dual space P as the joint kernel of simple differential operators, each one a power of a directional derivative. Various applications of this result to multivariate polynomial interpolation, multivariate splines and duality between polynomial and exponential spaces are discussed.
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http://digital.library.wisc.edu/1793/59106 
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