Polynomial splines as examples of Chebyshevian splines
Résumé
We consider geometrically continuous polynomial splines defined on a given knot-vector by lower triangular connection matrices with positive diagonals. In order to find out which connection matrices make them suitable for design, we regard them as examples of geometrically continuous piecewise Chebyshevian splines. Indeed, in this larger context we recently achieved a simple characterisation of all suitable splines for design. Applying it to our initial polynomial splines will require us to treat polynomial spaces on given closed bounded intervals as instances of Extended Chebyshev spaces, so as to determine all possible systems of generalised derivatives which can be associated with them.