Cardinal Hermite interpolation with box splines (Q1112269)

The authors initiate a study of multivariate cardinal Hermite interpolation: the interpolation of successive directional derivatives. It is assumed that the set T of directions satisfies a certain determinant condition and that each direction t occurs in T with even multiplicity. The cardinal Hermite interpolation is formulated in rather general terms and a procedure is given with a view to select the fundamental splines which describe the solution. The approach is in the Fourier transform domain.