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International Journal of Mathematics and Mathematical Sciences 
Volume 2003 (2003), Issue 33, Pages 2083-2095
doi:10.1155/S0161171203211091

Mean convergence of Grünwald interpolation operators

Zhixiong Chen

Department of Mathematics, University of Connecticut, Storrs 06269, CT, USA

Received 5 November 2002

Abstract

We investigate weighted Lp mean convergence of Grünwald interpolation operators based on the zeros of orthogonal polynomials with respect to a general weight and generalized Jacobi weights. We give necessary and sufficient conditions for such convergence for all continuous functions.