Article ID Journal Published Year Pages File Type
4608022 Journal of Approximation Theory 2009 12 Pages PDF
Abstract

Let Wpr(Bd) be the usual Sobolev class of functions on the unit ball BdBd in RdRd, and Wp∘,r(Bd) be the subclass of all radial functions in Wpr(Bd). We show that for the classes Wp∘,r(Bd) and Wpr(Bd), the orders of best approximation by polynomials in Lq(Bd)Lq(Bd) coincide. We also obtain exact orders of best approximation in L2(Bd)L2(Bd) of the classes Wp∘,r(Bd) by ridge functions and, as an immediate consequence, we obtain the same orders in L2(Bd)L2(Bd) for the usual Sobolev classes Wpr(Bd).

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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