The approximation order of box spline spaces Academic Article uri icon


  • Let M M be a box spline associated with an arbitrary set of directions and suppose that S ( M ) S(M) is the space spanned by the integer translates of M M . In this note, the subspace of all polynomials in S ( M ) S(M) is shown to be the joint kernal of a certain collection of homogeneous differential operators with constant coefficients. The approximation order from the dilates of S ( M ) S(M) to smooth functions is thereby characterized. This extends a well-known result of de Boor and Hllig ( B B -splines from parallelepipeds, J. Analyse Math. 42 (1982/83), 99-115), on box splines with integral direction sets. The argument used is based on a new relation, valid for any compactly supported distribution phi , between the semidiscrete convolution phi ast and the distributional convolution phi ast .

published proceedings

  • Proceedings of the American Mathematical Society

author list (cited authors)

  • Ron, A., & Sivakumar, N.

citation count

  • 7

complete list of authors

  • Ron, A||Sivakumar, N

publication date

  • January 1993