Let L n ½f denote the Lagrange interpolation polynomial to a function f at the zeros of a polynomial P n with distinct real zeros. We show thatwhere 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 ðÀ1; 1Þ that are not assumed analytic in any ellipse with foci at ðÀ1; 1Þ: r 2004 Elsevier Inc. All rights reserved.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.