Piecewise Smooth Spaces in Duality: Application to Blossoming

Given an (n+1)-dimensional space of piecewise smooth functions in which each basis has a non-vanishing Wronskian, and its dual space *, a canonical bilinear form is defined on × *, which provides a simple characterization of a contact of order rn. An intrinsic reproducing function is introduced, leading to Marsden-type identities. In the case of Chebyshev spaces connected with totally positive matrices, the bilinear form yields a general notion of blossom which can be extended to Chebyshev splines.