On the Hermite–Fejér Interpolation Based at the Zeros of Generalized Freud Polynomials

Abstract

This paper deals with a special Hermite-Fejér interpolation process based at the zeros of generalized Freud polynomials which are orthogonal with respect to the weight w(x) = |x| α e −|x| β , x ̸ = 0, α > −1, β > 1. We prove its uniform convergence for functions belonging to a suitable space of functions equipped with a weighted uniform norm.

Hermite-Fejér and Grünwald interpolation at generalized Laguerre zeros

“…By contrast, in particular the Grünwald operator based at the zeros of orthonormal polynomials w.r.t. exponential weights has received few attention in literature [3,13,17].…”