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Title of Journal: Sci China Math

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Abbravation: Science China Mathematics

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SP Science in China Press

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DOI

10.1002/ncr.4110351014

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1869-1862

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Approximation of functions on the Sobolev space wi

Authors: HePing Wang YanWei Zhang XueBo Zhai
Publish Date: 2010/02/13
Volume: 53, Issue: 2, Pages: 373-384
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Abstract

We discuss the best approximation of periodic functions by trigonometric polynomials and the approximation by Fourier partial summation operators ValléePoussin operators Ces`aro operators Abel operators and Jackson operators respectively on the Sobolev space with a Gaussian measure and obtain the average error estimations We show that in the average case setting the trigonometric polynomial subspaces are the asymptotically optimal subspaces in the L q space for 1 ⩽ q ∞ and the Fourier partial summation operators and the ValléePoussin operators are the asymptotically optimal linear operators and are as good as optimal nonlinear operators in the L q space for 1 ⩽ q ∞

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