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On Müntz Rational Approximation Rate in Lp Spaces

✍ Scribed by Wei Xiao; Songping Zhou

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
102 KB
Volume
111
Category
Article
ISSN
0021-9045

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A convex function \(f\) given on \([-1,1]\) can be approximated in \(L_{r}, 1<p<x\). by convex polynomials \(P_{n}\) of degree at most \(n\) with the accuracy \(o\left(n^{-2 i p}\right)\). This follows from the estimate \(\left\|f-P_{n}\right\|_{p} \leqslant c \cdot n^{-2 / p} \cdot \omega_{2}^{\var