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

  • S. B. Damelin (a1) and D. S. Lubinsky (a1)

Abstract

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

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References

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Keywords

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

  • S. B. Damelin (a1) and D. S. Lubinsky (a1)

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