Journal Title
Title of Journal: Constr Approx
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Abbravation: Constructive Approximation
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Authors: A Kroó J Szabados
Publish Date: 2013/10/26
Volume: 39, Issue: 2, Pages: 397-419
Abstract
Multivariate incomplete polynomials are considered on compact 0symmetric starlike domains Problems of density and quantitative approximation properties of such polynomials are investigated It is shown that density holds for a certain class of starlike domains which includes both convex and some nonconvex domains On the other hand a family of nonconvex starlike domains is also found for which density fails In addition it is also shown that on 0symmetric convex bodies in mathbbRd continuous functions can be approximated by θincomplete polynomials with the rate Oω 2n −1/d+3 Moreover if the convex body is the intersection of simplexes with vertex at the origin then this order improves to O omega 2f1/sqrtn
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