Article ID Journal Published Year Pages File Type
4606821 Journal of Approximation Theory 2016 24 Pages PDF
Abstract

We show that any compact subset of RdRd which is the closure of a bounded star-shaped Lipschitz domain ΩΩ, such that ∁Ω∁Ω has positive reach in the sense of Federer, admits an optimal AM   (admissible mesh), that is a sequence of polynomial norming sets with optimal cardinality. This extends a recent result of A. Kroó on C2C2 star-shaped domains.Moreover, we prove constructively the existence of an optimal AM for any K:=Ω¯⊂Rd where ΩΩ is a bounded C1,1C1,1 domain. This is done by a particular multivariate sharp version of the Bernstein Inequality via the distance function.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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