Let w be an Erdös-type weight on ℝ and let pn be the orthonormal polynomials with respect to w. We denote by xj, n the zeros of pn. For an interger ν≥2 and a continuous function f on ℝ, let Hn (ν;f, ·) be the ν-th order Hermite–Fejér interpolation polynomial for f based at xj, n, that is, Hn (ν;f, xj, n) =f (xj, n) and Hn (k) (ν;f, xj, n) = 0 hold for j=1, 2, …, n and k=1, 2, …, ν-1. We discuss a uniform norm of Hn (ν;f, ·) -f on ℝ and give quantitative interpolation estimates.
Sakai et al. (Thu,) studied this question.