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Constructive Approximation

, Volume 13, Issue 4, pp 569–583 | Cite as

Kergin Interpolants of Holomorphic Functions

  • T. Bloom
  • J. -P. Calvi
Article

Abstract.

Let D be a C-convex domain in C n . Let \(\{A_{dj}\}, \ j = 0,\ldots,d\) , and d = 0,1,2, ..., be an array of points in a compact set \(K \subset D\) . Let f be holomorphic on \(\overline D\) and let K d (f) denote the Kergin interpolating polynomial to f at A d0 ,... , A dd . We give conditions on the array and D such that \(\lim_{d\to\infty} \|K_d (f) - f\|_K = 0\) . The conditions are, in an appropriate sense, optimal.

This result generalizes classical one variable results on the convergence of Lagrange—Hermite interpolants of analytic functions.

Key words and phrases: Logarithmic potential, $\C$-Convex, Kergin interpolation. AMS Classification: 32A05, 32A10, 41A63. 

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Copyright information

© Springer-Verlag New York Inc. 1997

Authors and Affiliations

  • T. Bloom
    • 1
  • J. -P. Calvi
    • 2
  1. 1.Department of MathematicsUniversity of TorontoTorontoCanada
  2. 2.Laboratoire d'Analyse Complexe U.F.R M.I.G Université Toulouse III 31062Toulouse cedexFrance

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