, Volume 72, Issue 1, pp 203-221

Kergin interpolants at the roots of unity approximate C2 functions

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Abstract

We establish a new formula for Kergin interpolation in the plane and use it to prove that the Kergin interpolation polynomials at the roots of unity of a function of classC 2 in a neighborhood of the unit disc \({\mathbb{D}}\) converge uniformly to the function on \({\mathbb{D}}\) .