Abstract
LetAdj be a triangular array in a compact setX⊂C n . Forf analytic in a neighborhood ofX, letL d (f) denote the Lagrange interpolant tof at staged of the array. In the caseX is locally regular, we construct a continuous functionϕ satisfying the complex Monge-Ampere equation onC n −X, such that iff is analytic onϕ≤R forR>1 then, for someB>0, we have ∥L d (f)−f∥ x ≤B exp(−d logR. In particular, sinceϕ≤1 onX, iff is analytic onϕ≤1, then lim d ∥L d (f)−f∥ x =0.
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