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The Approximation Order of Box Spline Spaces

A. RonN. Sivakumar

出版	University of Wisconsin-Madison, Computer Sciences Department, 1990
URL	http://books.google.com.hk/books?id=oQmnPgAACAAJ&hl=&source=gbs_api

註釋

Abstract: "Let M be a box spline associated with an arbitrary set of directions and suppose that S(M) is the space spanned by the integer translates of M. In this note, the subspace of all polynomials in S(M) is shown to be the joint kernel of a certain collection of homogeneous differential operators with constant coefficients. The approximation order from the dilates of S(M) to smooth functions is thereby characterized. This extends a well-known result of de Boor and Höllig [BH], on box splines with integral directions sets. The argument used is based on a new relation, valid for any compactly supported distribution [phi], between the semi-discrete convolution [phi]*́ and the distributional convolution [phi]*."