Necessary and Sufficient Conditions for Mean Convergence of Lagrange Interpolation for Erdős Weights

Damelin, S. B. ; Lubinsky, D. S.

Canadian journal of mathematics, Tome 48 (1996) no. 4, pp. 710-736

Résumé

We investigate mean convergence of Lagrange interpolation at the zeros of orthogonal polynomials pn (W 2, x) for Erdös weights W 2 = e -2Q . The archetypal example is Wk,α = exp(—Qk,α ), where α > 1, k ≥ 1, and is the k-th iterated exponential. Following is our main result: Let 1 < p < ∞, Δ ∊ R, k > 0. Let Ln [f] denote the Lagrange interpolation polynomial to ƒ at the zeros of pn (W 2, x) = pn (e -2Q , x). Then for to hold for every continuous function ƒ: R —> R satisfying it is necessary and sufficient that

Détail

DOI : 10.4153/CJM-1996-037-1

Mots-clés : 42C15, 42C05, 65D05, Erdős weights, Lagrange interpolation, mean convergence, Lp norms

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