On two polynomial spaces associated with a box spline

Carl De Boor, Nira Dyn, Amos Ron

Research output: Contribution to journalArticlepeer-review


The polynomial space H spanned by 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.

Original languageEnglish
Pages (from-to)249-267
Number of pages19
JournalPacific Journal of Mathematics
Issue number2
StatePublished - Feb 1991


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