Journal d’Analyse Mathematique

, Volume 72, Issue 1, pp 203-221

First online:

Kergin interpolants at the roots of unity approximate C2 functions

  • Len BosAffiliated withDepartment of Mathematics and Statistics, University of Calgary Email author 
  • , Jean-Paul CalviAffiliated withLaboratoire de Mathématiques E. Picard, UFRMIG Université Toulouse III

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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\({\mathbb{D}}\).