Fractional Cone Splines and Hex Splines

الأصل · EN

We introduce an extension of cone splines and box splines to fractional and complex orders. These new families of multivariate splines are defined in the Fourier domain along certain s-dimensional meshes and include as special cases the three-directional box splines article:condat and hex splines article:vandeville previously considered by Condat, Van De Ville et al. These cone and hex splines of fractional and complex order generalize the univariate fractional and complex B-splines defined in article:ub,article:fbu and investigated in, e.g., article:fm,article:mf. Explicit time domain representations are derived for these splines on 3-directional meshes. We present some properties of these two multivariate spline families such as recurrence, decay and refinement. Finally it is shown that a bivariate hex spline and its integer lattice translates form a Riesz basis of its linear span.