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Application of Mhaskar-Prestin operators to the convergence of orthonormal expansions

✍ Scribed by H. P. Mashele

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
180 KB
Volume
283
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

Let I be either R or (–1, 1), and let W: I β†’ (0, ∞). Assume that W^2^ is a weight. We study the quasi‐interpolatory polynomial operators Ο„~l,n,m~ introduced by Mhaskar and Prestin, for Freud weights, ErdΓΆs weights, and the exponential weights on (–1, 1). We investigate boundedness of Ο„~l,n,m~ in weighted L~p~ spaces. We then use this result to show that

equation image

for even exponetial weights (Β© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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