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\({\mathbb{D}}\).
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Bos, L., Calvi, JP. Kergin interpolants at the roots of unity approximate C2 functions. J. Anal. Math. 72, 203–221 (1997). https://doi.org/10.1007/BF02843159
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DOI: https://doi.org/10.1007/BF02843159