Asymptotic convergence of degree-raising

It is well known that the degree-raised Bernstein-Bézier coefficients of degree n of a polynomial g converge to g at the rate 1/n. In this paper we consider the polynomial An(g) of degree ≤ n interpolating the coefficients. We show how An can be viewed as an inverse to the Bernstein operator and that the derivatives An(g) (r) converge uniformly to g at the rate 1/n for all r. We also give an asymptotic expansion of Voronovskaya type for An(g) and prove a shape preserving property of this polynomial. §