Article ID Journal Published Year Pages File Type
4607457 Journal of Approximation Theory 2012 5 Pages PDF
Abstract
For k∈{1,2,3,…}, we construct an even compactly supported piecewise polynomial ψk whose Fourier transform satisfies Ak(1+ω2)−k≤ψ̂k(ω)≤Bk(1+ω2)−k, ω∈R, for some constants Bk≥Ak>0. The degree of ψk is shown to be minimal, and is strictly less than that of Wendland's function ϕ1,k−1 when k>2. This shows that, for k>2, Wendland's piecewise polynomial ϕ1,k−1 is not of minimal degree if one places no restrictions on the number of pieces.
Related Topics
Physical Sciences and Engineering Mathematics Analysis
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