International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 33, Pages 2083-2095
Mean convergence of Grünwald interpolation operators
Department of Mathematics, University of Connecticut, Storrs 06269, CT, USA
Received 5 November 2002
Copyright © 2003 Zhixiong Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We investigate weighted 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.