Necessary conditions for weighted mean convergence of Lagrange interpolation for exponential weights

Abstract

Given a continuous real-valued function f which vanishes outside a fixed finite interval, we establish necessary conditions for weighted mean convergence of Lagrange interpolation for a general class of even weights w which are of exponential decay on the real line or at the endpoints of (-1, 1). (C) 2001 Elsevier Science B.V. All rights reserved.