Piecewise Smooth Spaces in Duality: Application to Blossoming Original Research Article

Given an (n+1)-dimensional space U of piecewise smooth functions in which each basis has a non-vanishing Wronskian, and its dual space U*, a canonical bilinear form is defined on U×U*, which provides a simple characterization of a contact of order r⩽n. 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.