Chebyshev-Schoenberg operators
Résumé
We show that a given space of splines with sections in a given Extended Chebyshev space gives birth to infinitely many positive linear operators of Schoenberg-type. As a consequence of the properties of Chebyshevian B-spline bases such operators are automatically variation-diminishing. Among other results, we show that the set of two-dimensional spaces they reproduce is stable under knot insertion and dimension elevation, and we establish a simple sufficient condition for convergence.