Dimension elevation vs Approximation by Bernstein operators
Résumé
Let us start with an infinite nested sequence of Extended Chebyshev spaces, each of them being assumed to possess a Bernstein basis. This situation automatically generates an infinite so-called dimension elevation algorithm. The question of convergence of the sequences of control polygons associated with given curves naturally arises. On the other hand this situation also automatically generates an infinite sequence of Bernstein operators all reproducing the same two-dimensional space. Again, the question of convergence of this sequence towards identity naturally arises. In this talk we examine the links existing between the two convergences, with still open questions.