A note on mean convergence of Lagrange interpolation in Lp (0 < p ≤ 1)

[摘要] Let w:= exp(-Q), where Q is of faster than smooth polynomial growth at infinity, for example, w(k,x)(x):= exp(-exp(k)(/x/(x))), alpha > 1. We obtain a necessary and sufficient condition for mean convergence of Lagrange interpolation for such weights in L-p (0 < p less than or equal to 1) completing earlier investigations by the first author and D.S. Lubinsky in L-p (1 < p < infinity). (C) 2001 Elsevier Science B.V. All rights reserved.

[发布日期] 2001-08-01

[效力级别]  Proceedings Paper

[关键词] Erdos weight;Lagrange interpolation;mean convergence;orthonormal polynomial;weighted approximation