Abstract
Let L n [ f] denote the Lagrange interpolation polynomial to a function f at the zeros of a polynomial P n with distinct real zeros. We show that f−L n[f]=−P nH e H[f] P n , where H denotes the Hilbert transform, and H e is an extension of it. We use this to prove convergence of Lagrange interpolation for certain functions analytic in (−1,1) that are not assumed analytic in any ellipse with foci at (−1,1).
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